I'm in a similar position, but I don't think it's reached the same level as yours, yet, mostly because although I think my feelings bother my DH, he can't really argue with the bad behavior.

I have twin stepsons, 11 almost 12. One of them is a drama queen. When he stayed with us for a week over the summer for the first three nights he had a screaming, crying meltdown (the first night this lasted for 90 minutes) because we had "too many rules" at our house (really, the only rule we had was that no one is allowed to stay up all night and watch YouTube on their tablet). He demanded to go home early and called his mom twice a day, but of course, BM was going away at the end of the week, so he couldn't go home early. Now, at least once during his weekends with us, he will decide he is unhappy with something or is embarrassed over something and he'll call BM and cry that his dad is being mean to him and ask her to pick him up. Then she sends DH a series of angry texts saying she wants to pick the kid up and demanding to speak to him to know that he's fine. He's always fine after calling his mother, because really, he just wanted someone to validate his feeling bad for himself and also likes the idea that his mother promises to send nasty messages to his dad (which DH ignores). He also has a habit of blaming other people when he does something wrong. I've told DH that it's difficult for me to like this kid. If he was my kid, I would let him have it over so many things. I think it bothers my DH, but as I said above, he hasn't openly said he's angry with me. I'm sure it's just bubbling resentment underneath, but it's not going to change how I feel. If this child was mine, he would either be in intensive therapy to deal with his emotional dysregulation or dealing with some serious punishment for trying to be manipulative (or both). As he's not my child, I can't influence his behavior, so I don't feel like I should bear the brunt of it.

I've basically disengaged from this kid. I don't ignore him and I'm nice to him, but I don't go out of my way to interact with him and I've called him out a few times when he's being really ridiculous. The kids don't usually bring me into it, not sure if this is because they're boys. I also think that this kid is sort of embarrassed for me to see him having a meltdown. I'm not enough of a parental figure for him to feel comfortable crying and screaming in front of me. Both of my SSs have a tendency to cry and meltdown in front of DH, but they stop as soon as another person enters the room or comes close enough to hear or see them. If my SSs did try to blame me for something, I'm not sure what I'd do. That would definitely make the situation more challenging.

Ultimately, I've told my DH that I expect him to manage some of the inappropriate behavior and have made it clear that I'm not ok with it. When the kid is having a meltdown, I've either walked away or gone in my bedroom to be alone, because otherwise, it would be really hard for me to not scream "ENOUGH!" at the child, which I know would just cause more drama.

I'm already preparing myself for when he enters the teen years and becomes truly PAS'd by his mother (right now, BM has just told him "your father caused the divorce" - even though she filed for divorce because she met another man...), but he still enjoys spending time with his dad, so he sort of forgets about that on occasion. BM is also overly dramatic and has full-on adolescent meltdowns when she doesn't get her way, so she's essentially teaching the kid that meltdowns and manipulations are acceptable behavior.

I don't think I have any good advice, other than to commiserate about facing the same issue. I know I will never love this kid...I'll be lucky if I still like him in a few years.

Disengage completely thats the only advice I have...sorry! Take time for yourself when they are over, you have already talked to your DH and explained why. It’s on him to spend time with his kids. No more trips with them etc. it’s terrible of course and sad but what choice do you have. Until your DH parents her properly, which may never happen, have to put yourself first. I can tell you that when I disengaged it took a while but my DH only then began to parent his kids properly. Not perfect by any means but when you start to feel that this is consuming your thoughts and your life is hijacked by a disrespectful kid, it’s time to disengage. It will feel weird at first but you will grow to love your Me time.

This girl is only 10. So sit down with her and her father and tell her you want to like her and do things for her however when someone is rude and nasty and mean you do not have to spend time with them. As she doesn't behave nicely and be polite and *use the good manners her parents have taught her* it is very hard to like her. And as you are her stepmother you do not have to do anything for her. You are not her teacher or her mother so it is your choice how much time you spend with her. This is the one time you let her know how you feel about her and how she can change it. Then she cannot whine that no one ever told herrrrrrrr.
Then send her on her way to think about it. She has been allowed to behave like this because she has never been directed not to behave this way. This should have been nipped in the bud when she was 3 yrs old and told to stop the crap NOW.
And DH will have to recognize her histrionics will alienate her from other adults when she won't even be nice to you.

*when I wanted my ssons to tow the line I would tell them that I knew their mother did not allow this behavior. Did I really know? Of course not! But it did not allow them to have the ability to divide. They could not do the mom/ stepmom thing. And when they would crab about their mother I would often agree with her decisions even if DH did not. No little shit child would divide and conquer. Also it will give your DH no ability to back out and be the good cop to your bad cop.*

these blended wedding ceremonies are where skids get the impression they are part of the marriage between husband and wife. this happened at my wedding to dh. the children should be part of the wedding party but not the actual ceremony. i regret listening to the priest about including the skids in the ceremony.

you have a right of choose who will be in your life and disengage from anyone who is bad energy. young children have a way to really mess up a parents marriage so dont underestimate them.

at least your dh has the balls to punish his daughter. many of us here have husbands who would placate the child and make their wives out to be the bad ones.