If he plans to come back to Thailand get his Thai passport sorted before you leave for the UK. You'll need to bring his birth certificate to the airport to show he was born in Thailand (hence no entry stamp).
The very first thing you need to do is get your UK Marriage certificate legalised by the UK Legalisation Office in Milton Keynes and then certified by the Thai Embassy in London. It's much easier to do this while you're in the UK. I'm sure someone else will advise you about the procedure once you're in Thailand.
I had always assumed that as kids were exempt from fines for visa overstays, the same would apply to fines for not doing 90-day reporting. Anyway, I guess the worst that can happen is it will be brought up at one extension and Dad will have to pay 2,000 baht!