Can we apply for our daughter’s dependent visa at the same time as our education visas in Thailand?

Just to emphasize that you'll need to buy a re-entry permit after you get your extension inked in your passport.

I think you misunderstand how the process works.

You and your wife get the ED 90 day visas, then after that you get the extension of stay when that 90 days runs down

AND THEN

you can have your daughter apply for the in country 90 day Non-O visa based on being the child of a parent enrolled in school here for 2000baht

She can't get the 90 day Non-O until YOU get your extension based on education.

The good news is there's no overstay fine for a child under 15, and they can't be banned when they're under 18.

So just let them overstay until you get your ED extension (after you got the 90 day Non-ED) and then bounce out and back with them to get on a NEW visa exempt entry so they can start the process of applying for the in country Non-O visa

You're lucky that the school can even offer that service because MANY schools do not offer visa support for children/family of their ED visa students.

Just wait it out, that's how the process works.

Nothing will happen to her on overstay, I know foreigners with children here on many YEARS overstay, there is no exposure to them or the parents

You just clear the overstay by exiting/re-entering to get on a new entry stamp so you can start the visa process for them once you can do it