I think this is the actual core of the problem with Regina’s redemption arc: she never does it for its own sake. All though the first half of Season 2, she was doing it for Henry, or for the town’s acceptance, or even - perhaps - to restore the influence she once held through fear. She never does it because she can’t live with what she did, or because she feels guilt over the pain she caused, or even because she genuinely wants to be a better person. Everything is motivated by attaining a goal - Henry, the town, and perhaps her own power.
Which is why she was so easily turned by Cora: she has no motivation beyond immediate material gratification to do this. She doesn’t feel badly about killing Leopold or Graham or countless others, or about the Curse, or about anything else. She hasn’t forgiven Snow and that was the feud that started this. She doesn’t have to like the town, and for self-professed good guys they admittedly didn’t give her much of a chance (which is a whole other essay) but she shouldn’t, essentially, have needed them to. She has no genuine remorse, that we have seen, for anything that she’s done. And that made her a fantastic villain in season 1, but it makes her redemption arc incredibly unstable.
In the end, she was trying to be good to get Henry back. And she realised that to do so she’d have to co-exist with Emma and Snow and Charming, and accepted that, for which I was very proud of her. But the moment those three stood between her and Henry and Cora provided a solution, she reverted to her old patterns. She wants Henry back and we’ve seen that Regina is an any-means-necessary kind of woman.
She’s also impatient: she wants him back and she wants him back now. She wanted Snow, Emma and Charming to help her and she wanted them to help her right away. She asks ‘what did it get me?’. If she’d wanted redemption, truly wanted to be good, then just being good should have been its own reward, and given her some peace of mind. She’s looking for a greater reward, and she won’t find it. She has a long road before she’s even able to understand that Snow and Charming are good because they want to be good, not because someone is giving out trophies at the end, or because they want people to like them.
She still has no empathy for the pain she caused them, no understanding that they hurt in the ways that she hurts, and because of that no remorse upon which to build a solid desire for redemption, that would be its own reward. They had a right to assume that she might have killed Archie: she’s killed before and she’s only been good a few weeks/months, time that Emma and Snow didn’t even see. If she understood the gravity of the pain she caused, she wouldn’t expect them to forgive her instantly: she’d understand that it will take time and patience and work. That’s the only mindset that will allow her redemption to stick. Until she understands that she hurt these people as much as others have hurt her, then she isn’t going to be able to feel sorry for what she did, or have any genuine desire to change for change’s sake. She’ll keep doing it all for Henry, and when it looks like it’s not working, she’ll change tack and try something else. That’s not a redemption arc, that’s a quest.
This scene shows perfectly why Snow will never forgive Regina, and why Regina will never ask her to. Even with her own redemption for crimes she committed entirely by herself, Regina sees herself as the victim rather than the perpetrator. And Snow, too, sees herself as the victim rather than accepting any responsibility for letting Regina fall back to Cora, although she is at least a little more justified, in my opinion, than Regina in this view. Regina never apologised truly, without hope or agenda. So Snow cannot forgive her truly, without hope or agenda. Remorse and forgiveness, like redemption, must exist in a vacuum: they have to happen for their own sakes to be true. A few good deeds don’t make up for years of murder, rape, and abuse, especially when she killed the woman in front of her’s father in cold blood, and proceeded to try to kill her too for a mistake she made in good faith as a child. A few good deeds don’t make up for that, especially when not accompanied by any genuine remorse or empathy. Snow will have a long way to go before she can understand where Regina is coming from - and this new dark side arc will help, I think - but Regina also has a very, very long way to go before she’ll see that forgiveness isn’t something she should expect just because she wants it, but something that needs to come organically from a long period of genuine hard work at being a better person for her own sake.