Actually, there is no Non-O for the reason of attending school. Also, no Non-O multiple entry (still valid) for reasons other than being a spouse to a Thai (there are a few very specific exceptions, though).
Now Doubtful your son has an actual multiple-entry Non-O visa. If he is studying at a real school, he could be on 1-year extension with a multiple re-entry permit. Or up to 3 months extension (incremental) if he is studying at a private school, such as a language school.
Check his current visa or stamp and make sure what he is on now, at least whether he has an entry stamp directly from a visa, or an extension (for whatever period).
He can enter Thailand being stamped on his new passport, using his current visa/extension on his old passport. But visa/extension cannot be transferred at entry point. He needs to go to the local office that issued his extension to transfer stamps once he is back to Thailand. Don't forget getting re-entry permit before leaving Thailand, and don't forget to bring his old passport back to Thailand.
Only at the immigration office that issued your current one-year extension. If yours was issued at Chaengwattana, you must go to the Chaengwattana office.
On the other hand, if you are on an extension for studying (just ED, NOT ED-plus), you need to leave Thailand once to enter on Non-B or as a tourist to proceed. Check your current stamp, and talk with your uni and new employer
, That sounds strange. You might get some other reasons. There are a lot of people in Bangkok who get a 60-day visit Thai family extension, then a Thai spouse extension and they are rather standard than exceptional. Those were already on entry on a Non-O visa marriage to a Thai or extension for the same reason, though.
"Completion of the TDAC will be mandatory for all foreign passport holders, including tourists, business travellers, and long-term residents. Exceptions apply only to travellers transiting or transferring through Thailand without passing through immigration control and to those entering using a Border Pass."