Switching transplant centers is pretty easy - just a matter of getting your records transferred to the new hospital and reminding the new hospital to submit a time transfer (which you will need to sign) through UNOS. You will have to go through the basic eval again, meeting with their particular line-up of team members. If any of your tests have not been done in a year, you will probably need to redo them. Oh, and they will always insist on doing their own bloodwork at their lab. It's a legal issue.
I have transferred twice. Yes, the hospital that I was exiting was not happy about it, but it's an awkward few minutes and then you are done. Take a deep breath, and tell them why you would be more comfortable elsewhere. When I transferred within the same city, I tried to be honest (to a point) with the nurse coordinator. I told her that every time I went to the hospital (USC in my case) no one seemed to know who I was or why I was there, and orders for tests were often an hour or more late in arriving. She was satisfied with that, because she was able to blame others. I felt it best to leave out the personality clash that I felt she and I had from the first moment I arrived. Time really depends on the hospital and how quickly they will see you, but I think it took about 6 weeks in my case.
When we left Cedars-Sinai for Nothwestern, the live-donor coordinator shouted at my husband (my potential donor). I had nothing but good things to say about Cedars until that moment. She shouted because we did not personally call her and tell her we were leaving, even though I had told them that I was moving to the Chicago-area.
I don't need IVIG which is their big, transplant specialty, so I have no idea why she thought we would bother flying 2000 miles to go to them when we can do this locally.
I can't remember what my husband said back to her, but you can bet it was cutting. I know it's often easier said than done, but if anyone is rude to you over this, tell them that you are going to do what makes you feel comfortable and that's the end of it.
I would visit the new hospital first to make sure you really want to do this, and that they have the services you need and will approve you. They will ask you why you want to transfer, and just give your reason and go from there.
Good luck!