I don't think it makes you a horrible person, or, frankly, different from anyone else on this forum, since what you're describing is very human. Where I part from you is in thinking that this creates a parallel between you and Regina.
Past a certain point, differences that might on their face be seen as just differences in scale, in my opinion, become differences in kind as well.
Let's take the example of theft. I think it is reasonable to draw an analogy between fairly petty theft - or even things like illegal streaming -- and theft of more expensive items. Yes, you're going to be punished more harshly for grand theft auto than for shoplifting but conceptually, both involve disregard for the property rights of another. The person who shoplifts might well be willing to steal the Ferrari if he thought he could get away with it.
On the other hand, I don't think we can draw a line between theft and someone who bilks loads of people out of their fortunes by running a Ponzi Scheme. Sure, it is arguably just theft on an even grander scale, but I don't think the logic of "Hey, I like that watch so I'm going to take it. It isn't fair that some people have so much more money than I do anyway" is comparable to the logic of "I'm building up relationships of trust with people over the course of years, while knowing that my actions will eventually bankrupt them." One requires selfishness and maybe some resentment, the other has passed into what I would consider sociopathy.
Yup, when people are hurting, it is natural, if ugly, to sometimes take it out on others, and even to want others to experience some of your own pain. And yes, part of the reason Regina is more destructive than the average person with these feelings is simply that she has the power to be more destructive. But first of all, most of us - except in petty and perhaps subconscious ways like maybe being rude to other people -- stop short of actually taking steps to actively harm others, even to the small extent we are capable. Yes, if a person loses her job, she might actually be kind of glad when a friend loses hers as well. If a new employer calls her as a reference, she might even wind up being less generous than she otherwise might, if not subtly undermining. Maybe she does this subconsciously, and maybe she does it consciously, but finds a way of justifying it to herself: "Well, I have to be honest. Julie really is late to work occasionally, and though she was good enough at her job, I don't know that I'd call her an excellent employee. It isn't like I said anything that wasn't true, or said anything so bad that she might not still get the job. And if not, I can't be blamed for honesty." And that isn't attractive, or kind, but you can do it and still be a generally compassionate and decent human being.
That's qualitatively different from, say, calling Julie's boss to falsely accuse her of financial malfeasance because you want everyone to be as unhappy as you are. Especially if, you know, she winds up being criminally prosecuted for it. Doing that is well beyond ordinary human fallibility, even allowing for the corrosive effects of power.
I'd also point out that a) Regina didn't just do this for a while after Daniel's death, she lashed out for years and b) that she did this even when she had a lot of objective advantages and privilege in life. I'm not saying that any of them negate the pain of Daniel's death, or growing up with Cora, but a morally normal person is able to maintain at least a modicum of perspective in assessing her situation in comparative terms. First of all, in the context of the world Regina lives in, while her mother killing her fiancé is still horrible, it isn't any kind of singular tragedy; as depicted, life in the EF is pretty grim for most people. Extreme poverty, violent deaths, unjust imprisonment - these are facts of life in the EF. Secondly, Regina has tons of other things going for her. Maybe her marriage with Leo - freely entered into, I might add -- wasn't a love match, but she was queen, living in a palace. Once she had killed Leo, she was solely in charge of a kingdom. That's a position that gave her a lot of agency in bettering her life in productive ways; instead, she continues acting as if - and presumably feeling as if - she is the most unfortunate and injured person in the history of humankind.
After the curse, her behavior becomes even less understandable. Regina has gotten literally everything she has been working for. It is understandable that that doesn't make her instantly happy and fulfilled. But she has a comfortable life, tons of power and, eventually, a son to love and raise. Even if she wasn't going to give up on the curse, you'd think this would be a moment to acknowledge "I've won; I've gotten my revenge; now I can work for my own happiness rather than sadistically hurting others." But from what we can see, she remains just as committed to causing pain as ever, even when it isn't necessary to maintaining her design. We don't know much of what she's been doing before Emma comes to town, but everything we see suggests that, in this reduced context, she's still finding ways of exerting petty power over everyone, including her own son.
This isn't a relatable extension of normal feelings.