Hi Chris I believe you are based in the UK. You can apply for a Non-O online via the online portal. But you also have unusual circumstances with the loss of their mother. The Royal Thai Embassy in London is fantastic and they will help you relocate to Thailand with paperwork.
Our daughter is now 6 and was born in the UK. So she had a UK certificate of birth and UK passport. I got in touch with the Royal Thai Embassy directly and they arranged for my daughter's Thai CoB and emergency passport so we could travel back to Thailand without visa issues for my daughter.
If you want the email of the lady I was in contact with please DM me.
Here's your visa link apply for a Non-O. When you arrive in Thailand extend the visa on the grounds of family support.
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