Once Upon A Time -- Regina Is One Twisted Sister
I don't think it's an overstatement to say that Snow White is the genesis for everything Regina became. She saved Snow's life and her reward was for that good deed to cost the life of the person she loved most in the world. Snow made a promise to Regina not to tell Cora about Daniel and Regina and she didn't keep it. Because of those two actions Regina learned that not good deed goes unpunished and deals are made to be broken.
That I've seen Regina hasn't made one deal with someone that she's actually honored. And it may go back to the deal she made with Snow not to tell her mother, Cora, about Regina and Daniel. Maybe she feels Snow secretly got what she wanted by telling Cora about Daniel, which she did, so now that's how she conducts business. I'm sure she derived a great deal of pleasure when she got Snow to eat the apple in exchange for promising to spare Charming, only to turn around and try to kill him.
Hansel and Gretel got Regina her poisoned apple and instead of reuniting them with their father, who she was holding prisoner in her castle, she sent the three in different places so they'd have to search for each other to find each other. And she promised things to Jefferson twice and back-stabbed him both times.
Regina also seems to have quite a daddy issue, as well. In the above mentioned cases of Hansel and Gretel and Jefferson, she tried to make the father's seem like they had abandoned their children. In Hansel and Gretel's case Regina had kidnapped the Woodcutter so she could manipulate Hansel and Gretel into going into the Blind Witches house to steal the apple for her. And with Jefferson, Regina manipulated him to feel he wasn't providing a good enough life for Grace so he'd help her, then she turned around and made him seem like he was bad for deserting his daughter. In both cases Regina seemed to be foisting her own relationship with her father on to Jefferson and Grace and Hansel and Gretel and The Woodcutter.
From what we've seen on Henry in regards to Cora, he was very weak and never really stood up to her. He didn't really do much to stop Cora when she levitated Regina in the air and wrapped some bands around her arms. He just stood there and did nothing. And when Cora accepted King Leopold's offer of marriage, his objection to what Cora was doing was weak-willed at best. Regina may have resented Henry for not controlling her mother and protecting her from Cora's viciousness. And now when she sees a father and daughter she puts her own experiences on their relationship and judges the father as being a bad father.
To be fair to Henry, he didn't seem to possess any magical power. So trying to stand up to his wife wouldn't have done any good. Of course, Regina can't see that. Just like she can't see that Snow was just a child and you really can't trust a child to keep a secret. Unfortunately, Regina doesn't think that way. It's all about what was done to her with no understanding for the reason it may have happened.
The sad thing about Regina is she still craves love and if she got it she might change her ways. Unfortunately, the ones she craves it from don't love her back, and the ones that do love her she doesn't really value their love for her.
Regina could have just killed Graham when he tried to pass off the heart of a stag for Snow White's heart. She took Graham's heart and made him her sex slave. The fact that she continued being Graham's lover in Storybrooke kind of hints that Regina might have had real feelings for Graham. There was great irony in what Regina did to Graham when he left her; it was exactly the same thing Cora did to Daniel. Cora did what she did to Daniel because he was the reason Regina was going to leave her, and Regina did what she did to Graham because he was going to leave her.
Regina also seems to long to be a mother. She wanted Hansel and Gretel to come and live with her in her castle and forget all about their father, but when they refused she casted them back into the forest when she could have easily reunited them with their father. And in Storybrooke she was still stinging from their rejection as she tried to get Emma to take them out of Storybrooke, knowing something bad would happen to them if they tried to leave town.
We now know Regina had some control over the lives of the people she trapped in Storybrooke. She gave Grace a nice happy family life, while she made Hansel and Gretel homeless orphans. Once you cross Regina, she never can let it go. She could have just as easily have given Hansel and Gretel some nice family home, too, but she made them homeless orphans still trying to find their father who they'd rejected her for.
Of course, Regina thought if she raised a child from a baby, then she'd finally have the love she craved. Only that didn't happen when Regina adopted Henry. He went looking for his real mother and seems to have no real feelings for Regina, at all. Of course, one has to ponder why when she was adopting this boy baby she decided to name him after the father she murdered? It seems to be further evidence of Regina's twisted feelings for her father.
When she rescued her father in Wonderland, it seemed pretty obvious she loved him. But when Henry was urging her to let go of her anger and hate so the two of them could be happy together, she voiced resentment that he was finally concerned about her. Like she felt it was too little too late. It seems obvious she both loves and hates her father. It may have been the part of her that hated him that allowed her to rip his heart out so she could enact the curse. Yet maybe it was her love for him that made her name the child she adopted after him.
Of course, the big question is if Regina found someone that truly loved her, could she change back to the Regina who loved Daniel and saved Snow's life? But if someone really did love her, would she use them as she's used Sydney who does love her? Does Regina only love and want those show don't want her back as some kind of protection so she never betrays the love she shared with Daniel? Even when she was sleeping with Graham, she still held dear the memory of Daniel.
Regina is a very twisted sister. She has no understanding or empathy when she feels someone has wronged her. Instead she strikes out at them wanting to punish them. When she enters into a bargain with someone she betrays them before they can get a chance to betray her. And even though she wants someone to love her, the two men who did love her, her father and Sydney, she used for her own means. With her father, she used his heart to enact her revenge against Snow White and with Sydney she used him to get rid of her unwanted husband.