Regina obviously hates Emma (in a similar vein to how Voldemort hated Harry Potter). She abhors the idea of Emma trying to reclaim Henry.
Regina fears the return of Snow White and Prince James’ child based on the exchange between her and Rumple in FTL. Rumple warned Regina (in ep. 2) before the curse was enacted:
Rumple: Nothing can stop the darkness, except, of course, their unborn child. You see, no matter how powerful, all curses can be broken. Their child is the key.
I think Regina already has her suspicions about who Emma is in SB. Mr. Gold toyed with Regina at the end of ep. 2:
Mr. Gold: Perhaps you should have come to me. If Miss Swan is a problem you cannot fix, I’m only to happy to help, for a price, of course.
Regina: I’m not in the business of making deals with you anymore.
Mr. Gold: To which deal are you referring?
Regina: You know what deal.
Mr. Gold: Oh, right yeah. The boy I procured for you. Henry? Did I ever tell you what a lovely name that was? However did you pick it?
Regina: Did you want her to come to town? You wanted all this to happen, didn’t you? Your finding Henry wasn’t an accident, was it?
Mr. Gold: Whatever do you mean?
Regina: Where did you get him? Do you know something?
Mr. Gold: I have no idea what you’re implying
Regina: I think you do. Who is this woman, his mother, this Emma Swan?
Mr. Gold: I would say you think you know exactly who she is.
Interestingly, there is a medieval looking tapestry of a white unicorn in Rumple’s estate in FTL (ep. 12). Rumple seems to be very scheming. One instance, he seems to be offering to help Regina “fix her problem” and yet, it seems like he is secretly planning to call upon Emma with the favor she owes him. In ep. 8, Desperate Souls, Rumple does help Emma get elected town sheriff. He seems to be playing Regina and using Emma to do it. He is the one who procured Henry in the first place, in order to attract Emma to SB.
"That’s how you know you’ve really got a home. When you leave it, there’s this feeling that you can’t shake. You just miss it." Neal Cassidy