Show your tickets, explain the original error as you see it ... then say can I have 7 days ... and I will pay the other fine upon leaving... Show them the outbound tickets right off ... And do you have a Thai friend that understands your situation and can explain it ... Thai to Thai always helps IF that person fully understand what is going on ...
This is not a regular Thai Consulate as is normally thought of. This Consulate is one of the many around the world called Royal Thai Honorary Consul Generals. They are contractors.
For just a tourist visa from the Thailand Consulate in LA -- not likely to be a problem for someone from the UK... If you have not filled up your passport previously with Thai visa entries and visa exempt entries ... you should be fine.
I think you are going to have to go to immigration and see if they will reverse the Visas back to where you have the ED and the child has the non O. It is possible you will have to go back to the Embassy/Consulate that issued them. I do no not see how you can proceed as the Visas are now done . An ED Visa for a child is not going to work