Thanks for your reply, so it's take some time for me to get back to you.
You will have to apply for an EEA family permit in order to secure your leave to remain in the UK to work. You will need to apply for it before you travel and must submit the appropriate documentation to the UK embassy closest to you:-
If you are not married then you will have to show that you are in a "durable relationship", usually this would mean having cohabited for greater than two years but in view of the length and nature of your cohabitation you may be able to prove this element by submitting documentary evidence of your relationship during this time (eg. Witness statements, correspondence, joint utility bills etc) then you should be fine in convincing them of your ummarried partner status.
If you marry in the Seychelles and then apply from the US to the UK embassy there then you need only show your marriage certificate. You will have to include your child in the application as your dependent.
Once you have come to the UK on your family permit you will be eligible to apply to the UKBA for a residence card which confirms your right of residence in the UK on the basis of your marriage. It will either take the form of an endorsement in your passport or as a separate immigration status documents confirming your right to reside here for 5 years. At the end of this time you will be able to apply for a Permanent Residence here if you wish subject to the residential restrictions in place.
If this has been useful please kindly click accept so that I may be rewarded for my time. If you do not click accept your money stays with the site and I do not receive any credit for the time I have taken to answer your question.
I will answer your follow up questions you may have.