I've been confused for a while about Regina's intentions towards Henry. She'll pretend to care about him, and then scar him emotionally just to win a battle against Emma.
In episode one, Emma had asked Regina if she loved Henry, and Regina replied "yes," yet Emma used her "super power" and knew Regina was lying. Emma is rarely wrong with it, and some of the things Regina does makes it seem like she really doesn't l’amour him. Which begs the question, why even adopt a child?
I think it's because Regina was lonely, she wanted some companionship in a world where everyone is basically walking zombies of the curse. But I believe Emma's senses that told her Regina was lying about loving Henry. Regina takes care of Henry and buys him things, but doesn't give him the emotional care that a mother should. And usually when she does, it's an act ou ploy to get at Emma.
I'm still not sure her true intentions towards Henry, but I do believe he's there because she's lonely. I won't go so far to say she loves him, but I think she cares for him. She cares for herself a lot plus though.