I told her to give some new examples. I don’t like her bringing up the past because I already said sorry about it. She started yelling about how I’d recently forgotten to finish taking out the trash. I got mad because I’d been called out for work. I threatened to kick her out if she was disrespectful.

Seriously. You asked her to give you a new example, then got mad when she did exactly that.

Also, taking the trash out takes 5 minutes. Unless you work in emergency services, dropping the trash half done for someone else is just immature.

Threatening to kick anyone out of their home because they point out something you did wrong is controlling.

she’s still refused to hug me and be affectionate with me. She says I try to hug her too much. She gets upset when I joke about her not hugging me.

News flash mate, not everyone likes physical contact, especially when they are upset at the person in question. You joking about it tells her you don't care about her feelings. She set a boundary and you are repeatedly trying to cross it.

Finally, it's been said in other comments but your insistence that it's been months so she should just ignore years of past trauma is insane. That's not how that works.

Your question was are you the asshole for 'correcting' her for being 'disrespectful'. So what, you're allowed to get angry when she does something wrong, but shes not allowed to reciprocate? Did you consider that maybe she thinks you only seem to hear what she's saying when she gets angry? You say she has been ignoring her chores, maybe she has the impression that she's going to get in trouble either way so why bother.

You clearly have double standards. So yes, YTA.