Yes, the confrontation sucks! I think that as long as everything is understood upfront there shouldn't be a problem.
I would maybe send her an email this weekend quoting the agreement and advising her that $XX is due prior to care on Monday in order to her child starting their day at your daycare in order to bring her account up to balance. And that's all I'd say. I wouldn't threaten to not care for the child etc.
When she comes on Monday, if she doesn't offer it to you right away I would say something like "$XX is owed to complete last weeks payment" If she argues or doesn't have it, then refuse care. "I'm sorry, but my policies states that I can't continue care for a child until the account is where it should be" And take it from there. Sounds like she's the type that might get snippy, and all the better if she does. At least if she get's snippy you can let her know that she can contact you by phone to finish the conversation if she'd like, but it's not a conversation you're able to have during daycare hours and ask her to leave.
I know... all is easier said then done. Try not to stress over it and enjoy your weekend. You deserve to get paid and if you have a contract you need to enforce it. If you let it go, what is she policy is she going to break next?