Was it like this before your son was born?  If you dislike her for no other reason other than she is not your child, you are the problem.  It sounds like you are going to therapy.  I hope that will help you.  This is no way to live.  I hope you didn't have a child with him if you already felt like this about his daughter.  It is just not fair to any of them.  If your therapist isn't helping, find a new one.  

I kind of understand where you're coming from my ss10 is very rude, whiny, and entitled. Things he's done in the past make it hard for me to even want to be in the same room. I dread the time they're here and I feel the stress and anxiety the whole time. 
 

therapy may help you understand how to cope. But you're not alone. I would really like to enjoy the time with the sks. But I constantly am waiting for them to do something terrible. 

Something about your previous posts reminds me of "bait-and-switch" relationship stories.  Usually it's the DH agreeing to a 'theirs' baby until he snags SM & reneges a few years later.

Seems as if you moved to be with DH & SD --- now with your own child you wish to return home w/DH without SD. 

Cutting a steer out of the herd?

You're not alone in your perspective. Many of us would have secretly liked to cut our SO out of the herd of his family & prior commitments.  Our reasons are good.  I'm not certain how ethical/fair it is, tbh.  I'm guilty of wishing to move away w/my SO, away from the crazy & I could totally justify it.

Ultimately, I realized SO & his boxcar of bullshit responsibility that he's dragging along are combined. I can't seperate him. Those responsibilities that I wished he'd shrug ... help to define him.

I would also suggest therapy to get to the root of your problem with her. Some people will say "you're the problem", and that may be, but i don't fully buy that. The fact that you are on this site and feeling guilty about it says that you are not a "wicked stepmom" just wanting to get rid of her for no reason.

Really think about what specific things about her annoy you. They may not be her fault but there may be a solution so that you can all live together. Is it certain behaviors that can reasonably be corrected, or can steps be taken to where they don't affect you as much? Is it her presence in certain areas of the house at certain times (your bedroom for instance?) Is your partner different toward you or less attentive when she is around? That would be expected but maybe you could identify ways he could still meet your needs while also parenting her?

You seem to want to fix this, so that tells me you care. You are not a bad person. Stepparenting is hard even in the best of circumstances. Think about what's happening when you have these bad feelings. Sometimes people have bad feelings for what seems like no reason. But there is always a reason. Identify the reasons and you can take steps to correct them. 

So, make a different choice.  You are entirely in control of how you choose to feel and act around your SKid.  You were clear, you dislike her for no other reason that she is not your child.  You are choosing to be miserable, not only during her visits but also for days after she returns to BM. By choosing to be miserable, you are making your DH miserable, your own daughter miserable, and you are destroying your family.

So... as I said. Make a different choice.  Moving does not kill a Skid and dispose of them permanently.  While it can significantly change the blended family dynamic, long distance visitation has its own challenges to deal with that have to be effectively managed to not alienate the Skid and not alienate the prior relationship breeder who brought the Skid to the new marriage.

So, make the changes you need to make, own your choice to be miserable, do something about it, and stop that! 

"My husband and I are planning on moving cities within the next few months and while I think that would help solve my issues, it would create issues for him and not having his daughter 50% of the time."

That kind of speculation is not helpful. You don't know what kind of (if any) issues it would create for him. Maybe he'll be fine and things will work out for everyone. Wait and see.

" it would create issues for him and not having his daughter 50% of the time"

Things may not fo the way you hope they will. He might be able to continue with 50% (or almost) by having her less often but for much longer periods. Think about it.