Working in the USA as a RMN

There is no such thing as an RMN in the US. US nurses are trained and licensed as generalists. You will need to have documented didactic (classroom) and clinical hours in adult and pediatric med-surg, psychiatry, and obstetrics in order to be eligible for licensure in any US state.

You are welcome to work exclusively in psychiatry; plenty of us do, but we are all licensed as generalists.

There are a bunch of threads here about the difficulties UK-trained RNs have with getting licensure in the US. You may want to do a search for them and have a look. Basically, your best bet, always, is to train in the country in which you expect to practice. Do you have to go to school there? If you know you're coming back to the US, you can't wait to go to school here? Immigration/citizenship status has nothing to do with it; if you go to school abroad, even as a US citizen, you will be considered an internationally-educated graduate and will have additional paperwork and "hoops to jump through" not just for initial licensure, but any time you want to get licensed in another state for the rest of your career.

I agree with elkpark. If you know for certain--or are fairly certain--that you are relocating to the US for good, then you'd be a lot better off going to school in the US because it would eliminate most licensure problems. A lot of state BONs are very strict when it comes to international graduates, and will have to deal with a lot of extra frustration and paperwork when you apply for licensure. If your UK education is lacking in certain areas because you specialized in PMH, you may find it very difficult to take the missing coursework in the US because US schools don't really offer nursing courses a la carte.

In addition, should you get licensed in one US state doesn't mean the other BONs will automatically endorse you in: see California for the best example of this. As elkpark said, you're going to have to repeat the entire paperwork process for each and every state that you wish to endorse into.

Best of luck whatever you decide.