Without a doubt, ask for your money. On the occasion that a parent hasn't handed over their money to me on payday, the first thing I say is "do you have my payment"? Then they run to the car because they forgot it there, or whatever, but they need to pay me that day. If you don't mention it, they'll think you don't care.

Since you've had prior issues with this family, can you not tell them that you will be collecting payment at the beginning of the week as opposed to the end. That way if they don't pay on Monday, then they receive no childcare for that week and you won't be left at the end of the week out of money.

Good luck!