I don't know what you do when you clean the vaginal area. Perhaps I'm misunderstanding because of past experiences in use of the term vaginal area. If you go between the vaginal lips she will feel pain or just an ucomfortable feeling. Wiping between the lips is usually not neccessary. If feces is in the area then it may be neccessary to look and if you see feces in that area clean that out as gently as possible.
Actually keeping a babies vaginal area clean is not so important that you have to keep struggling with her. Vaginas are self cleaning and a baby has very little secretion compared to adults. She is also not exposed, as an adult is, to things that will cause difficulties if they are not removed.
I've seen lots of babies who don't even get their diaper changed often enough and they don't have a UTI or irritation between the lips. They may have a severe diaper rash that does appear in the crotch but the actual vaginal area was OK.
If you give her a bath, that area will be clean enough without physically washing the area. Swishing water does the work. Or you can have her wipe between the lips with her hands. Don't use soap or if you do use just a little amount of a very gentle soap and quickly and gently rinse. Soap often stings. But remember the vagina is self cleaning and the creamy stuff that clings to the clitoris is normal, healthy stuff and can be left.
Have you tried telling her what you are doing and why in a sing song voice? You could also teach her to wipe her Dolly's between the legs space.
If you are just wiping the external pubic area and she objects try not doing it for awhile to break the cycle. Just give her a tub bath each day if you're concerned about diaper rash or urine odor. At this age vaginal secretions do not have an odor.
When you return to wiping do it quickly and make it a game. Perhaps give her a wipe so that she can wipe too. Sing with her. Perhaps about what you're doing and how you think she is feeling. Acknowledging that you know she's frustrated or angry might help.
My granddaughter began to not want to lie down after she began walking and especially when she was busy doing something else. I changed her diaper where she was and often while she was standing. If she did lay down she could continue playing with the objects that had been absorbing her attention.
I didn't always wipe her, either. She remained healthy. Running from me became a game. I would catch her and say, "Now I've got you. Lets get this over with." Sometimes she fussed and almost always she squirmed. I just did the job as quickly as I could. Sometimes she would lay down by her choice and sometimes she remained standing.
Holding a child down using 3 people turns the diaper change into a power struggle and a big deal. She's screaming and the adults are working hard to make her like what she doesn't like. How would an adult or older child feel if someone held them down and they couldn't even sit up? Babies have very little if any power and when you hold her down you take away the little bit of power she has just recently learned that she has; that is to move around. Once the issue of wiping became serious and has to be done she becomes frightened or angry or both. Anger often covers up fear.
Stop with the holding her down and wiping for a couple of weeks. Let her know that you're not wiping for a few days because it upsets her so much and explain why it's important to wipe in baby terms. then, when you start wiping again explain to her what you are doing when you externally wipe her. Kids seem to respond to a sing song voice when they won't respond to words given in a serious tone.
When she's objecting to changing her diaper give her a choice. (change it now or after we stack the blocks 6 blocks high?) Ask her if she wants to lay down or stand up? Give her choices. Make a game of it so that it's not so serious. Hold two wipes, one in each hand, and ask her which one she wants you to use.
If she still struggles big time, skip the wipe and let her up. It's possible that once she realizes that you will let her up that she will gradually become less angry. Give her power. Often we are in a hurry and just want to get the job done. We suddenly pull them away from their play. How would an adult feel and react if someone made them stop doing something enjoyable and they didn't understand why it was so important to be interrupted. When the adult protested they continued moving them. I don't know if you do the changing by removing her from what she's doing but I've seen it happen over and over.
There will be many causes for power struggles. Some are not worth beginning or continuing. I don't think cleaning her vaginal area is one worth continuing. Get out of the power struggle mode before resuming the cleaning.
Another idea. Perhaps pull ups would be easier to use. You can just rip the sides to take them off. She could actually do that. And then she could help pull them up.