First off, yes this woman is asking too much because YOU LET HER. Your daycare, your rules! I would not be taking requests from parents to give their child crackers in the stroller because we have a set snack time as is. And changing into pjs at naptime? No way. Send your child in clothes that are comfortable enough to sleep and play in and there should be no need to change them.
She doesn't seem to be taking you seriously about her child's aggressiveness. I would say flat out no for the journaling and having a sit down chat with her about your expectations and what you are doing and your side to change this and what she should be doing at home and that if you don't see improvement in this child's behavior within 2 weeks (or your chosen time frame) then unfortunately you will not be able to provide care for them. You have a responsibility to look out for all the other children in your daycare and it's not fair to the other families to be dropping their child off in an environment that is unsafe and unpleasant. And to be honest-it sounds like you would be better off without this client. One of the most important things if you want to stay in the daycare business for a while is to have boundaries and stick with 'em. If you don't, families will walk all over you and take advantage of you.