Can we take our kids with overstayed visas out of Thailand for a holiday and then return for a visa exemption?

No problem for kids under 15.

If kids of the age you mentioned are overstay they can go and come back to thaipand and dont have to pay any fine also

𝗪𝗲 𝗮𝗿𝗲 𝗼𝗻 𝗮 𝗗𝗧𝗩 𝗮𝗻𝗱 𝘁𝗿𝗶𝗲𝗱 𝘁𝗼 𝗴𝗲𝘁 𝘁𝗵𝗲𝗺 𝗮𝘀 𝗱𝗲𝗽𝗲𝗻𝗱𝗮𝗻𝘁𝘀 𝗯𝘂𝘁 𝗮𝘀 𝘄𝗲 𝗮𝗿𝗲 𝗮𝗹𝗿𝗲𝗮𝗱𝘆 𝗶𝗻 𝗧𝗵𝗮𝗶𝗹𝗮𝗻𝗱, 𝘁𝗵𝗮𝘁'𝘀 𝗻𝗼𝘁 𝗽𝗼𝘀𝘀𝗶𝗯𝗹𝗲.

Well you could LEAVE thailand with them, and apply for the DTV's at any nearby consulate showing you as the parents already have them and they'd be approved pretty fast I'd imagine

𝗪𝗲 𝗮𝗿𝗲 𝗻𝗼𝘄 𝘁𝗿𝘆𝗶𝗻𝗴 𝘁𝗼 𝗴𝗲𝘁 𝘁𝗵𝗲𝗶𝗿 𝗲𝗱𝘂𝗰𝗮𝘁𝗶𝗼𝗻𝗮𝗹 𝘃𝗶𝘀𝗮𝘀 𝘀𝗼𝗿𝘁𝗲𝗱 𝗳𝗼𝗿 𝘁𝗵𝗲𝗺, 𝗯𝘂𝘁 𝘁𝗵𝗲𝘆 𝗮𝗿𝗲 𝗶𝗻 𝗼𝘃𝗲𝗿𝘀𝘁𝗮𝘆. 𝗔𝗻𝗱 𝗻𝗼𝘁 𝗷𝘂𝘀𝘁 𝗮𝗻𝘆 𝗼𝘃𝗲𝗿𝘀𝘁𝗮𝘆, 𝗮𝗻 𝗼𝘃𝗲𝗿𝘀𝘁𝗮𝘆 𝗼𝗳 +𝟭𝟴𝟬 𝗱𝗮𝘆𝘀.

𝗪𝗲 𝗵𝗮𝘃𝗲 𝗿𝗼𝘆𝗮𝗹𝗹𝘆 𝗺𝗲𝘀𝘀𝗲𝗱 𝘂𝗽 𝗵𝗲𝗿𝗲,

Who told you that you royally messed up?

There is no fine for children under 15 on overstay and no banning for overstay on children under 18. Your children are not the first foreigners to overstay, I know foreign children here on multi YEAR overstays.

Bounce them out of the country by air or land (they won't be fined for overstay, just get the stamp in their passport about it) and back in to get a new free 60 day entry stamp.

Then you could apply for the in country ED visa thru the immigration office where you live with documentation from the school.

You're not royally messed up at all.

You've got young foreign kids on overstay,

It's not a big issue at all

It's not a big problem either (other than you have to get the OFF the overstay to get any visa issued in country)

either go and apply for the piggy back DTV's at a nearby thai consulate, OR

just bounce 'em out and back to get them off overstay and on to a free stamp entry 🙂