Can mom just sue for this in small claims court in Lee County Florida?
I don't see why not, but winning in small claims court would just result in another court order. I suppose the advantage would be that it would be a court order to pay a specific amount of money, so the next step of getting a court order to garnish his wages or levy his bank account would be straightforward (if Mom knows where he works and/or banks).
Has Mom considered signing up for the child support enforcement services of the Florida Department of Revenue? I could find no mention of any fee on their website, so it's quite likely that signing up is free. They don't specifically address whether they enforce things like paying for daycare expenses, so she should ask that question if she hasn't already. If she signs up and they take over, then Mom would no longer be able to decide whether to cut Dad any slack in the future.