So with your sponsor you can go through the UK/EU line? (sorry to be dense)
Yes, because you need to go through immigration together as a family, and because your spouse is a UK citizen, you can usually go through the UK/EU line together.
Same goes when you enter the US... you both go through the same line together, usually the US passport line, because one of you is a US citizen.
However, when travelling alone, if you are not a UK citizen, you are not entitled to go through the UK/EU line, because you don't hold a UK/EU passport(and vice versa with US immigration).