I'd tend to agree with RobM that physical abuse in spanking fiction just doesn't work out well. Even if spanking isn't physical abuse (depends on who you ask, and I am
not going there) it's very much
like physical abuse, so it can make your readers uncomfortable. I think it can be made to work (just about anything can be) but you'd have to have Shakespearean levels of skill, and even then you probably wouldn't get it right.
Instead, I would recommend replacing the "physical abuse" with more psychological abuse. For example, rather than the bio mother hitting the main character, have the bio mother do some of the following things (the intensity at which any of the below would be done, would of course be up to you):
1. Blame the protagonist for things that aren't the protagonist's fault.
2. Curse out the protagonist.
3. The bio mother was inconsistent. Sometimes she'd blow up at the protagonist, other times she'd take it in stride.
4. Often the bio mother would yell at/punish the protagonist without making it clear what it was the protagonist did wrong. Any efforts by the protagonist to find out would just get a "you know what I'm talking about!" and more cursing out.
5. Never explains why a rule is important.
6. Sometimes, even after the bio mother was done venting, she might not forgive the protagonist, in the sense that she would often refer back to something, or bring it up.
Meanwhile, for the character's new parents, basically for everything (or most everything, depending on how flawed you want to make the new parents) that the mother did, have them do it completely differently (I've never had children, so I don't know if any of the below is "right." But if these kinds of things happen in a spanking scene in spanking erotica, then I tend to believe it when the spanker says "This hurts me more than it hurts you."):
1. The parents try to learn about mitigating circumstances before punishing the protagonist.
2. During the punishment the parents never directly insult the protagonist. This can be a little bit tricky, because you also want them to emphasize that whatever the protagonist did was wrong. Basically, have the new parents give gentle, but precise constructive criticism. At the same time, they're emphasizing that they love the protagonist, and they hate having to punish her, but it's for her own good, etc. etc. In short, they're not punishing her because of
her they're punishing her because of an
action and they know that she's better than that action.
3. The parents make sure the protagonist knows the rules ahead of time, knows what the punishments are, and applies them consistently.
4. The parents make sure the protagonist understand which rule was broken.
5. The parents make sure the protagonist understands why a rule is important. For a simple example: "Running into the street without looking is very dangerous. If you're not careful, a car could squash you flat as a pancake." vs "Don't run in the street! I told you not to, and I know what's best for you, so I'm going to punish you if you disobey me!"
6. When the punishment is over, the parents forgive the protagonist, and never bring it up again (unless there's a repeat, maybe). You could even have an exchange the next morning, where the parents are serving the protagonist breakfast, making sure she has her school lunch, etc. as if nothing ever happened. The protagonist, thoroughly confused, could be like "But aren't you still mad about last night?" and the parents could say something like "No, of course not. You broke the rule, you were punished, you learned your lesson, the matter's closed."
One advantage of making the abuse less physical and more psychological is that the abuse the girl suffered is
nothing like her new punishment. The abuse was random, lingered, cruel, and focused more on keeping her down, then helping her grow. Her new parent's punishment is predictable, over and done with, and geared towards helping her grow (in the context of spanking erotica. I'm not even going to touch real-world implications).
As for the scene itself, follow RobM's guidelines. From a purely erotic point of view, I tend to find compliant spankees kind of boring

, but in the context of your story, that's easily the best way to go about it.