At first I wasn't sure how that would work, but then I thought about it, and yeah -- say, in FTL, Regina just wanted to learn a spell to hide from Cora's magic, instead of turning fully to Rumplestiltskin. Once the containment spell couldn't recognize her, she went all runaway bride and then abandoned magic. She just wanted to be free, but Cora was determined to give her daughter power -- thought that once she'd tried it, she'd have a taste for it. So since Regina didn't want magical power, Cora set about finding a way to send her to a world where she'd have the ultimate power in a non-magical town, with everyone she felt had given her insufficient respect subject to her.

Meanwhile, Regina had settled down somewhere quiet and met a perfectly nice guy that was helping her finally move past Daniel's death -- perhaps a widower, who could understand not wanting to totally abandon the memory of a loved one, but not to reject a new love when you meet them. Then Cora shows up and is all "Pft, he's not good enough for you. Casting a curse to give you power now." and killed him.

So Regina arrives in Storybrooke pregnant with Henry and stuck as mayor of a small town where everyone is miserable, and any attempt to resign will have a similar result to someone who tries to leave town.