What are the steps for extending my daughter's stay in Thailand and legalizing documents, and do I need to send my passport for their visa application?

Hi everyone, I am after some advice. I am currently working in Thailand and I already have a non B working visa. My daughter (6 years old) has recently joined me and has 30 days allowed to stay in the country. My son (4 years old) and husband will join me in August, we all hold British passports. I have 3 questions.

1. What is the procedure to apply for an extension for my daughter and what documents will I need? She has no exiting flight as by September I am hoping to have obtained her visa.

2. I need to get documents legalized/notorized. I have been told I can only get this done in Milton Keynes England, is this true? Does the embassy not do it here? If that's the case I would need to post the documents from Thailand to London - correct?

3. The application that needs to be filled out for the royal Thai Embassy requires a passport sent + copies + photographs. Does this mean mine even though it's my children's birth certificates I am sending. I have been told it's because I will be the main visa holder that it's mine only.

I appreciate your help.