I don't think you are the subject of an Exclusion Order. These are normally only issued to keep out terrorists or people with extreme views. It looks like you were just removed as an illegal entrant, presumably because you had no visa for the UK.
But I am amazed that you didn't prevent that simply by applying as a Family Member of an EEA national for a Residence Card. You could not have been refused one just because you were illegally in the UK.
You should now apply to the British Embassy in Bangkok for an EEA Family Permit. This will be valid for 6 months, and once you are in the UK you can then get a Residence Card valid for 5 years. The Family Permit is issued on the basis that you are the wife of an EEA national who wishes to "exercise his Treaty rights" to live and work in the UK. The only grounds on which it can be refused is that they show that you are in a "marriage of convenience", i.e. that you got married simply to get residence in the UK.
Perhaps there's something you haven't told us about the circumstances of your marriage or the removal from the UK. But on the facts you have given it should be fairly easy for you to sort this out. Have a look at this page and work your way through the relevant links:-
http://www.ukvisas.gov.uk/en/howtoapply ... snationals