Once you have a spousal visa to live in the UK, you can come and go as you please, and travel as much as you like, and there should be no problems.
If you have been coming into the UK on a visitor visa so far, then each time you leave the UK your visa becomes invalid, and then you are issued with a new one when you come back - that is why you are questioned and given hassle, because each time, they have to establish whether you meet the requirements for a visitor visa... so when you come back, you have to show that you are not living in the UK and have no plans to live in the UK, that you are not spending more than 6 months in 12 months in the UK, that you have enough money to support yourself without working while in the UK, that you have a return ticket, a job, a home and a life to return to in the US after your visit, etc.
But once you have a spousal visa, you will have permission to live and work in the UK for 2.5 years and you won't need to get a new visa each time you enter the UK, so you shouldn't have any trouble leaving and coming back.
