Can my family get a student and guardianship visa after arriving in Thailand on a visa exemption?

Okay if you hold US passports there is no such thing as a "visa on arrival" You either BUY a visa from a thai consulate in the US before you come here OR you show up with out a visa and get stamped in FREE for 30 days on what's called a "visa exempt" entry.

You are correct you can get ONE 30 day extension on a 30 day visa exempt entry.

Now whether your husband has enough time to enroll in a school, pay the tuititon, get the documentation and get a 90 day ED visa issued is between him and the school.

AND

Whether you can get the 500K baht in a thai bank account in your name only and then apply for a 'guardian visa' to take care of a foreign child here will hinge on whether the day care can get the child an ED visa <- unless I'm mistaken the child has to be on a long term visa (ED etc) for you to use them as a reason to be here

Please do NOT hi-jack other threads 🙁 .

I split your comment out and made it's own post because you asked a LOT more than just about the one 30 day extension you can get on a visa exempt entry