A.J.
WOW.... first of all, the audacity of your SIL to tell you when to have your daughter's Bday is not appropriate. With that said, I do have a few people in my life that I have to hold my tongue and make dumb concessions for so I feel for you.
7 years old is old enough to be in on a decision like this. My son just turned 8 and while I normally don't give him more than A or B decision making power, I did give him some creative reign over his birthday and it turned out wonderful. I would use this as a great teaching opportunity with your daughter. In a positive way, let her know that there is a scheduling issue with her birthday and her cousins dance recital and ask her what she would like to do about it. Give her all the options you mentioned above, without editorializing how you feel about your SIL's request and see what your daughter wants to do.
If she is ok with her cousins not attending the BIG party on her birthday and wants to do something special later, she'll tell you. Either way, it is not your SIL's decision, and you shouldn't have to be put in the position to decide between your daughter and niece.