1. Unless your husband is your business partner and provides hands-on care, I'd discuss daycare issues less with him.
Providers losing in small claims court is a rarity, you'd have to be egregious. This is a simple no pay = no stay issue. Nothing more.
2. I'd tell her she must pay for the two days per week until September, then five days per week following that,
as tuition is not based on attendance if she wants to keep the slot. If she won't pay, she can't stay, the contract is void and deposit is forfeited. Really simple, IMHO.
3. I'd get rid of your part-time option, completely. One kid, one slot, one tuition rate, operating hours available, attend at will.
4. 2 kids sharing one slot is already luxury care, don't assume she isn't already expecting to pay.