Wow. It does sound like for whatever reason they need care desperately.

It could be that they suddenly got offered a job and have to start Monday or that their current provider terminated or they terminated their provider. I would give it a chance.
Him saying to hold the spot just means he wants you to keep it warm for him. He could be saying that to several other providers as well just so he can pick what daycare he wants.

When is the interview?

I would interview....but with a wary and suspicious examination to see what kind of feel/vibe I get and what sort of answers are given about the sudden need on such short notice.

good luck