Upvote:4
"given that it's a gay relationship" - CBP is uninterested in this detail.
You will be evaluated as an immigration risk just like everyone else.
"I'm also planning to visit my own family who lives in the U.S." - then make this your opening statement provided it is in fact true. You should have their address and know at least the town where they live.
Upvote:8
You do need to document how you will be supported while in the US, but that is probably not the main problem you will face.
Someone with both family and a boyfriend in the US is likely to be seen as high risk for overstaying. You will need to convince the US authorities that you really do intend to return to the UK at the end of your planned trip.
Do you have a job you need to return to? School or college? Other commitments, such as family members you look after? Property you own? You should carry evidence of anything that ensures you will go home.