Melissa has explained the most likely reasons for your daughter's aggression and I whole heartedly agree with her suggestions for handling it.
My grandchildren are now 5 and 8 and are still hitting, kicking spitting every day. Once Chase was mobile and getting into her territory Monet began pushing and hitting him. She was 3 1/2 or 4. She still complains that she has nothing that is hers only. They do share a bedroom and most of their toys are kept in the same places but she does have some toys that do not have to be shared and many that her brother is no longer interested in playing with.
One reason is that Chase does get a whole lot more attention than Monet because he is a special needs child. At 5 he is still unable to speak so that he is easily understood. Just the ordinary interaction of asking what would you want for a snack takes more time with him than with her. He has learned to compensate by taking your hand and leading you to and pointing at what he wants. But first it's important to take time as often as you can to make an effort to understand what he said and then repeat the word correctly, ask him to copy what you said. Even to me that feels more personal and does take more time then asking what do you want for a snack and handing it to her. I've noticed that sometimes when she's unhappy her speech becomes less clear than it usually is.
Babies learn how to get the attention they need and negative attention is better than no attention. Hitting brother does get your attention and for Monet her mother's attention.
Jealousy is a big reason for hitting. The older child is jealous whether or not we think she has reason to be. It is appropriate to give the younger child hugs and sympathy to model the appropriate way to respond to hurting someone. And she does need consequences because hitting is not acceptable.
The reason time outs are not effective is that we've only dealt with one part of the issue. We've shown her that hitting isn't appropriate because it hurts brother who then deserves supportive attention. But we haven't shown her that we're aware that she has these feelings and doesn't know how to handle them. He gets some special attention. She gets a time out. His needs are met. Hers are not.
It is important to separate the two of them, to not allow her to hurt him, to show her that hitting hurts and we expect her to not hurt him. I think tht is consequences. The purpose of consequences is to teach. She knows that she is not supposed to hit. She wants your attention. She also has anger created by the jealousy and she doesn't know how to express these feelings. That's why we also say use your words. At 2 1/2 she doesn't have enough verbal skills or even enough understanding to be able to adequately use her words to relieve the tension that is causing her to hit. And brother is unable to respond to her saying I'm angry because you took my doll.
My 5 yo grandson still responds with hitting when his sister says she's angry and want's her doll back. Probably because he doesn't have adequate language. He does often say it's my turn which makes sister angry because she already feels that he gets "more" turns that she does.
This is part of the reason that it is so important that you spend quality time with her when he's not there. You need to separate them and show your daughter that her hitting, etc. is not acceptable. Separating them does that. Giving her a "time out" in her room which allows her to move around allows her to work off some of that energy. Having toys to distract her helps point her in an acceptable directions. But this action doesn't change her feelings of jealousy.
Before she can learn better ways of handling her anger she has to know her feelings are OK even tho she reacted to them inappropriately. That is a difficult concept for a 2 1/2 year old to learn. She doesn't know that jealousy is a big component of her angry. She hits because she's angry. So does he. Do we put him in a time out? Probably not, at 17 months. We don't expect as much from him as we do from her. Reality is that there are reasons for their anger and are at different levels of ability to learn how to deal with their feelings.
A time out without at some point giving her some sympathy for how she's feeling only makes her angrier. She "knows" that you prefer brother; otherwise you'd show her some sympathy and awareness that you understand and accept her like you treated brother with understanding of his feelings.
One way of helping her feel that even tho brother gets extra attention ( she doesn't understand the difference in their needs) is to spend time with her when she doesn't feel that she's in competition with him. With time she will feel more secure in your love for her and feel less like he's replaced her in your heart. As Michelle said love is spelled t-i-m-e for children.
You don't have a whole lot of time so how do you spend one on one time with her? The cuddling for 10 minutes or so after he goes to bed is a good way that doesn't take up so much of your time. You could also do something with her while dad takes care of him and vice-versa. Take a walk, go to the playground. The parent with him can leave the house and she can "help" make cookies. Dad can keep him occupied in another room reducing her awareness of him. The two of you could color together. Her coloring will be really messy and not look like our concept of coloring but it will be her concept and she'll feel your approval. Tell her what a beautiful picture she's made. When you do it with her away from brother you're telling her she is just as important to you as brother.
Soon brother will benefit from his time alone with you. As he gets older and more verbal you will discover that he's also jealous of her. Because She's big and can do things he can't. As he becomes more independant you will spend less time with him and he'll think she gets more attention. It is common for both children to think the other child gets more attention, more things, is the favorite, etc. Sibling rivalry. This is the beginning of their expression of rivalry. You can lesson some of that jealousy by spending one-on-one time with both of them. It's important to find ways of showing them the many ways in which they're special as an individual. And this is one of the more difficult tasks of parenting because our time is limited. We have to find a way to schedule individual attention into our days. Does your husband have to spend long hours at work? I just reread your message. He can't take one child and you the other if he's not there. I've known many people, mostly men, who were workaholics. This condition is similar to the super mom concept. We expect so much of ourselves that we don't find a way to spend time with our children. When we are home we're so tired that we're not able to have quality time with our family.
I know first hand about super moms and workaholics. I was trying to be a super mom and didn't realize it for many years. I didn't really get it until after my daughter was grown. I became so stressed that I had to cut back my work hours to half time. I was our sole financial source. Working less meant spending less. That is difficult.
fortunately I had adequate money to still have a comfortable life. Many families need both parents working just to get by.
If your husband isn't able to have time to share the one on one time with the babies can you arrange to do it some other way? Exchange baby sitting time with another mother for example. Right now Monet has a friend whose mother has her over for the afternoon. They have a swimming pool. I recipricate by taking them ice skating and having ice cream.
Find a responsible teen to watch one while you have the other child for an hour. My daughter lives in an apartment. A couple of pre-teens loved babies. They came to the apartment and played with my granddaughter. My daughter could then do other things. (Monet was an only child then.) She was nearby if there was a problem and she didn't have to respond to Monet's need for attention. The girls didn't expect payment. This was play for them. We did have snacks for them and thanked them often.
If you don't have girls in your neighborhood you could try recruiting someone thru the school. This may not be easy to do and will require some creative thinking.
One of your friends or your husband's co-workers may even be willing to watch one for a short time without pay. I babysat for a co-worker an evening a week when his and his wife's schedules required them both to work and I loved it.
If you go to church, letting people know your situation may open the door for someone to watch a child or give more suggestions on how to make one-on-one time possible.
I wrote this thinking that you could get help from your husband. I'm sorry that I didn't remember that he worked long hours and that my suggestions for one-on-one time are not possible. I'm too tired to go back and edit. but I'm sending this anyway because the importance of finding a way to lesson your daughter's stress and improve her coping skills is important.
Talking about it when she is angry won't help. I'm not able to listen when I'm angry. And she doesn't understand what you're saying because her brain isn't mature enough to think in an abstract way. She knows that she is not supposed to hit. She doesn't know how to express or reduce the strength of her feelings any other way. She still feels jealous and insecure. She's angry but it's not the more simple anger that results from every day disagreements. Her anger is fueled by her jealousy. Responding to the reasons for her anger is more complex. She does need consequences for hitting but she also needs understanding and concern for her how she feels. This meets the need for attention as it also reassures her that she does have a place in the family. My grandchildren are still hitting, kicking, spitting much more often than they might be if we had found a way to know and meet their individual needs as toddlers and preschoolers. Because of Chase's disabilities and because he is a boy (It is common for parents to prefer boys without even being aware of it.) he does get more attention and understanding than Monet does. Learning how to balance so that each child feels as important to you as the other is important to you is a big challenge and often difficult to conquer. I'm glad that you are aware and wanting to learn!