you make a copy of the data page and the last entry/exit stamp on the DTV of the old passport (the one the DTV was issued under)
Put it with the copy you already have of the PDF print out you got from the thai consulate (that IS your visa) and show those copies with the new passport when you stamp in.
They will note you got the DTV issued on an earlier passport and stamp you in for 180 days on the new one when you arrive.
That's it, you show those copies when you stamp in to thailand for the duration of the DTV
Did you go out and talk to the people at the PR section at Chaengwattana (Section D) long before you're going to turn in your documentation?
I believe they would have told you that you should keep your Non-B extension and dependent child extension during this process.
post on the Thai Citizenship group and ask. Hands down that is the best group about Permanent Residence and acquiring Thai nationality on the inter-web today
The fact she's born in thailand as a foreign child doesn't matter at all 😕
AND
no matter what passport control tells you there is no overstay fine for children under 15 and no overstay banning for children under 18. They can't deny the child entry NOR can it cause you any issue as a parent of a foreign child on overstay. I know foreigners here who have children on multi-year overstays who exit/re-enter without any issues.
Your employer is a little confused as far as how the process works.
Your child can CAN get a 90 day Non-O visa based on being the family member of a foreigner who legally works here issued inside the country at the immigration office where you get your extension done for 2000baht.
The child cannot be on overstay when you apply, AND they need a minimum of 15 days left on their current free stamp entry because the application goes under review for 2 weeks before you go back to get the Non-O visa and new 90 day stamp inked in
Once that 90 days runs down you would apply for a yearly extension of stay that matches your employment extension stamp for 1900baht at the immigration office. Then every year when you get your new extension you get a matching extension for the dependent child
no you aren't going to be able to stamp OUT of thailand a day before your flight and then hand around in departures for a day before you board your flight 🙁
just show up, check in, stamp out and leave the country when you're supposed to?
Good luck with your travels, don't even know how this post managed to get ON the visa advice group, BUT we wish you well