I need some advice on a drop-in/back up care client. Thanks in advance!

So I had a parent contact me on Wednesday for care this coming week only as back up for her new regular provider. I agreed to it and we met Thursday, everything seemed ok, not great, but I figured for a week it was no big deal. So Friday afternoon I got a call for a job interview on Monday - Late notice, I know and I felt horrible, but I told the parents, including back up parent, Friday evening that I'd be closing at 2 on Monday.

Then I get a reply from back-up parent, basically stating that she cannot leave work early on her first day back (after some time off). I understood her frustration, gave her the website for a provider down the road, and offered to email another. No response. I heard back from the other provider today, so I sent her a message telling her to let me know if she wants to contact her, I'd give her the providers number. Still no response. That was 2 hours ago.

I don't even want to take her child on now tbh. I'm really suspicious of her getting off in time to pick her son up. This will either make me late for my interview or I'd have to leave my husband in the position to look after him until she gets here. And I don't reLly want to put him in that position with a parent who is already peeved.

I'm thinking of writing her back (and I'd like to have a record of what's been said) telling her "hi ___. I understand your frustration regarding early closure on Monday, however there are still things we need to discuss prior to drop off tomorrow. If you are unable to pick up by 2pm, or unwilling to discuss this matter further, I am not comfortable providing care for ____ this week."