Just incase anyone is interested before admin close comments. You can apply from abroad via post and require the usual documents for a Non Imm O based on marriage. They will accept printed online banking statements for proof of funds (website shows 3 months worth) and the turn around has been noted to be pretty fast. There we go, all questions from the OP answered.
Perhaps I should have, it would have saved a lot of misconception and speculation on everyones, including your behalf. However it's still irrelevant to the OP. Had I wanted an O-A I'd have said so. Had I wanted to send the passport from Thailand id have also said so. Perhaps not jumping to conclusions and focusing on the questions asked in the original post is also a suggestion. Apart from Ryan who's sent me an inbox (being a friend of mine) everything else has been a waste of time. Luckily Ryan managed to focus on the OP rather than speculate and I got all answers I require.
Okay, I have entered Thailand on my passport (1) which I will exit with. I'll arrive in Saudi Arabia on passport (2) making passport (1) redundant. I'll send passport (1) for a Thai visa and get it sent back to Saudi Arabia. I'll exit Saudi Arabia on passport (2) and fly to Thailand and enter with Passport (1) containing the new visa....pretty simple. I neglected to mention any of this as it's all pretty much irrelevant to my question and all very confusing for the purpose of getting the info I'm looking for.
You should be able to extend a visa exempt entry or a tourist visa by 60 days for the purpose of visiting family, rather than 30 days for purpose of of tourism. Same price1,900 Baht.
I have done this several times before I was married to the mother of my half Thai children.
I believe I just had to show birth certificates along with my extension application. I'm unsure if your child is of Thai nationality but it may also be possible to do it if they're in Thailand studying on a visa and you can prove this with the correct documents.