On the contrary. Henry would like nothing better than for Emma to take custody of him. And to see Emma fighting Regina for him. Henry believes Regina is the evil queen and also believes Emma is the savior. That fight is what Henry has been trying to instigate all along.
I agree but I think for Emma to actually get custody of Henry she’s gonna need to turn to Mr. Gold again for help. She was fed up at that point when Regina had Sydney take the fall I was glad to see her take a stand and actually call Henry her son.