Can I enter Thailand on an exempt status and apply for education and guardian visas later?

𝗖𝗮𝗻 𝘄𝗲 𝗲𝗻𝘁𝗲𝗿 𝗼𝗻 𝗮𝗻 𝗲𝘅𝗲𝗺𝗽𝘁 𝘀𝘁𝗮𝘁𝘂𝘀 𝗮𝗻𝗱 𝘁𝗵𝗲𝗻 𝗶𝗻 𝗠𝗮𝘆 𝗮𝗽𝗽𝗹𝘆 𝗳𝗼𝗿 𝘁𝗵𝗲 𝗲𝗱𝘂𝗰𝗮𝘁𝗶𝗼𝗻 𝗮𝗻𝗱 𝗴𝘂𝗮𝗿𝗱𝗶𝗮𝗻 𝘃𝗶𝘀𝗮𝘀?

You shouldn't have a problem getting in visa exempt entry then applying for the in country 90 day Non-ED visas for the children. There should still be plenty of time left on the children's 60 day free stamp entry to have time to apply for the in country Non-ED visas

However, with that being said, I am doubtful you'll be able to get the in country 90 day Non-O visas based on "raising foreign children enrolled in school on an ED visa" (guardian) because as a rule the immigration offices require the children to have their year extension based on education BEFORE they'll issue in country Non-O's to the parents.

You'll have to check with the immigration office where you will live/stay to see their policy on it

Also another thing to keep in mind is that 'guardian Non-O' is allowed only one per child, SO in order for parents to both be on guardian visa/extensions you need two children enrolled in school AND you each need to bank 500K in a thai bank account in your name only to get the in country 90 day Non-O issued and it has to be in the account for 30 days to get the yearly extension.

Still should be no issue for all of you to come in visa exempt entry and go from there.. The school will (should) know what's what for the children's ED visas and your Non-O guardian ones

Best of luck with it (y)