How can I extend my Non-Immigrant O visa for one year while applying for parental rights in Thailand?

You can get the 90-days Non-Imm-O Visa based on having a half Thai child, by showing the birth certificate with your name on it, when applying on the Thai embassy or consulate.

However for the application for a “1-year extension of stay based on raising a half Thai child”, you will need the parential rights approved by a Thai family court. And this process might take some months to complete.

You could set the approval process into motion before you go back to the UK by June, and when you return, you can either return with a 90-days Non-Imm-O again, but also on a 60-days Tourist Visa, and from there do the extension or, for the later, the conversion to a 90-days Non-O. Money 400K in a Thai Bank account is required, and you said you are complying with.

So actually everything is a question of correct timing

>I wanted to know if I apply for 1 year extension of stay, how long is the under consideration period?

Sadly, the length of the "under consideration" stamp depends on the immigration office, and how many visas they have to process. Generally expect two weeks or thereabouts :(

>Also we were not married when our daughter was born, how would I go getting parental rights?

You *MUST* get parental rights before you can apply for a one year extension of stay based on raising half-Thai children. You can get this either by marrying the child's mother, or by approval of the courts. Different provinces have different requirements.