I don't know if Carter was pushed into the background by Vala or if Tapping had lost interest like Richard Dean Anderson did, though I assume the former because she later joined Atlantis.
Nope, she did not choose to go to Atlantis, her contract forced her too. I really need to find that Gateworld interview that she did. She said she rather not have Sam go over to Atlantis but that the she was under contract and had no say. It's why she isn't in all of the Atlantis episodes in season 4 and why she isn't in season 5.
This is what Amanda Tapping said before season 4 of Atlantis...
"I am contractually obligated to the franchise for a year. I knew at the beginning of Season Ten that it was a possibility that if SG-1 went down that I might be doing some Atlantis. They exercised that option, which is fine."
She seemed so excited!