Yeah, she wanted Emma out of Storybrooke. She was hoping that when she left, that she would just stay out of Storybrooke. But it wouldn't have worked. Anyone remember the Pilot, a wolf stood in the middle of Emma leaving storybrooke, and so she swerved and hit the sign. Plus she knew she had to return Henry's book as well, so she couldn't have left anyways. 

i always thought emma could leave anytime she wanted because she wasn't cursed and she was the savior.

First, I like the Regina motive.  It make sense and fits with Regina's MO at the time.

Actually, I am starting to wonder if Emma WAS able to leave prior to breaking the curse.  It seems that Regina was able to come and go when she got Henry, and was otherwise satisfied to stay put.  Henry was able to leave to get Emma, but never tried to leave on his own any other time.

The one time that Emma tried to leave after arriving was when she had to swerve to avoid the wolf.  She got to the town border with the Zimmer kids, but her car conveniently broke down as I recall.  Now, whether that was Emma trying to get the father to take the kids, or the border 'curse', or some combination of the 2, is up for interpretation.  But my guess is that once Emma was in Storybrooke, she became just as much a part of the town as anyone else, and sufferered the same coming/going limitations.  And let's face it, she may have been raised in the LWM, but she is a native of the EF, though she was only there for a few hours.

Once the curse was broken, anyone COULD leave town, so long as they were willing to lose their memories.  Emma was a free agent in that regard, since she did not have false memories. And Henry was born in the LWM. Only Gold and Smee ever crossed the line without losing memories due to Gold's little memory concoction.  Hook never technically crossed the line until after the Manhattan incident, and since he did not have false memories, he was as much a free agent as Emma in that regard.

Another point is that August, once he came to town, never tried to leave prior to the curse breaking.

Now, that does leave me wondering if anyone is free to leave under Snow's Curse.  At first, there were flying monkey's patrolling the border, but that was Zelena's doing, not the curse.  Maybe that will be something explored in the next season.

^ I like your thinking, but I would like to point out that her car didn't conviententally break down; she pretended it did to get the kids' father there. My point is that Emma could leave, but no fairytale characters could– therefore, if something bad should happen to Ava and Nicholas, it stands to reason that something would happen to Emma along with them.

I know THEY couldn't leave, so it may explain the car breakdown. Convienently, Emma wanted their birth father to take them in, anyways.