I like honesty but I can understand that sometimes that can be uncomfortable esp if it's a gut feeling vs a hard reason.
If you said you have gone with someone else, and then advertise, it doesn't look very professional in my opinion.
I think I would just message her and say what you said.
"Upon considering our prior conversations, I don't feel that I am a good fit for your needs. With that in mind, I feel it would be unfair to waste your time for our scheduled meeting and therefore would like to cancel it. I wish you all the best and I'm sure you will find a wonderful carer who is a perfect fit for your family."
If you don't feel you can be so direct, I'd maybe consider having the interview after all. You never know, they might surprise you. Although normally my gut feelings about someone are right, there has been the odd time where I felt a family might be a pain in the butt but then I've met them any way and they've taken on board fully my terms and conditions and never let me down. So sometimes, we do get it wrong.
I wouldn't waver the deposit - but it might be that they didn't budget for one and when she said she couldn't afford it, that was a gut reaction to an expense she hadn't considered. Since she set up an interview anyway, it's possible that she's managed to raise those funds since we was made aware of them.