If you have a copy of your child's birth certificate, get it translated and signed and stamped, and apply for a uk passport, then in Thailand apply for thai passport, my 2 daughter's are classed as duel nationality, no visa needed,for your child. Then start the long lenthy process of visa for your wife, good luck
I had the same situation earlier this year my non o visa didn't come before I flew , I entered on a 30day visa exempt, extended for 30 days in the mean time visa email came ,not forgetting it's valid 3 months from issue, I went to Vietnam, came back to Thailand and activate my visa, then extended for 60 days ,with the options of extending for 1 year based on marriage.