If you married your Thai wife in America and file for divorce in Thailand is the divorce valid in the USA and how do you "register" or record the divorce in America.

The divorce will be valid in the US, but a divorce settlement (how property is divided, etc) might not be recognised and could under circumstances be challenged.

The US doesn't have a central register for marriages. You will have to ask the state where you got married if they will register the divorce. Otherwise the Thai documents will proof your divorce, after being legalised by the US embassy.