We took a parenting class that said to let each child have some special toys that they don't have to share. I think the advice is good when the 1-1/2 year old is trying to take away from the 4 year old for the 4 year old to give a different toy. Also, do you ever get out alone with the 4 year old? Can you leave the 1-1/2 year old with a babysitter or when your husband comes home go out with the 4 year old even if just for a half hour.
One mistake I know is that I concentrated too much on the baby and the babies needs and my daughter was feeling left out. Not saying you do that, but it's easy to do. Or maybe you can play games with the 4 year old when the younger one sleeeps.
I think as parents we try to solve our kids battles too much. How about if you tell the 4 year old I know you can work this out. You are very smart and I know you can figure something out in a nice way.
Do your kids like to color, maybe give them each their own color book and say they can't take or color on the other ones. What about teaching them to play Go Fish or the memory game with cards where they turn them all upside down and try to match them up. If you have a computer, I am sure you can look up and find many more games. Also, at this age play dough was one of my kids favorite toys. I would put them at the kitchen table and let them create. Water colors are also good.
What about taking them to parks that have the water that sprays up. Desert breeze has one with animals that spray water. I don't where you live, or if you have a little yard space but what about a little swimming pool that blows up or something like that.
My kids loved being in the pool/sprinklers often. Watch carefully and use lots of sunscreen.
Do you like crafts. There are many crafty things you can do too. If you have a computer look up www.familyfun.com. My kids loved those little pot holder kits - this would probably entertain your oldest.
I meant to say the arguing/fighting is so normal at this age. Don't look at it if it's your fault or there is something wrong. I think if you don't focus on it and don't comment on it as much maybe it will help. I know I tried too hard to solve all my kids issues thinking if they were fighting I was doing something wrong, but kids are kids and they feel things are always unfair, they get jealous and they don't like to share. If you try to allow them time to solve it (and step in only when necessary- don't let them hurt one another). They will learn some valuable coping skills. This is hard as a mom to do though.
One other idea, have you looked into play groups where you can get out of the house with other moms and kids close to your kids ages? This is very helpful - you need some mommy time for yourself too. And the kids would probably love to play with kids their own age.
Take care and God bless, I hope this helps,