R.,
I don't want to discourage having her evaluated but I have a three year old that has acted that way for over a year and there is absolutely nothing wrong with him... they said it is called "spoiled rotten syndrome".
Me and his father got a divorce in August. He was the "anything goes" parent. Just in less than 2 months there is a big difference.
They told me not to send him to another room at first. Just set him in a chair in the corner where he cant see the tv. If screaming or crying last longer than 1 minute. Then you remove them from the family room.
I make him carry his little chair to his room and sit in it. He is not allowed to come out untill the crying/screaming stops AND he is calm. Of course, he loves school. They have no problems...they say he is the best kid in the class.
The improvements have been great. Her mom is doing the right thing about meal time. That was an issue that I had to correct too. He has started eating what we eat...not a lot of it...but he is tasting and liking!!!
Another aspect that you might consider is that she may be copy catting what she sees out of her sister. My 2 year old daughter repeats everything my 3 year old son says. Which is ok...she has a large vocab. but she also tries to pee standing up and likes to wear his clothes and play with only his toys. She never plays with anything of hers.
I don't know it could be a possibility....
I don't know the severity of her Asperger's but she probably gets some special attention or care taken with her....maybe that is what your 5 yr old is after.
Good luck!!! It seems to me that you have your hands full.