giving her only the choice of who gets to brush first is excellent advice. and YOU need to brush her also!! She does not have the dexterity to do a good job until she can tie her own shoes.. make sure you use non/flouridated paste!! (Oral B or Tom's of Maine) and only put a smudge of it on. Eating too much flouride can give her brown spots on her permanent teeth.
Sometimes it takes two adults to do this--one gets her to lie down with her head in your lap while you see into her mouth, you brush, and the other holds her hands down. Brush for the whole ABC song, or some other song she likes. It's a battle, but one you must win, unless you want lots of trips to the dentist. By the way, she should have her first dentist appointment already. If she doesn't really brush well, she could have cavities already.