I don't mean to sound harsh, but I think the break up should have stuck. You knew that you did not want to be a step mom. And being with someone only a year, especially when they have kids, is not long enough to really get to know the person and the dynamics of what you are in for.

You say that she's a good kid but that there is something about her that makes you angry. I think you need to figure out what that is, if you want this marriage to work.

I get it. I've never wanted kids, either, so being a step mother was not exactly on my list of things to do. But my SD was a pretty good kid and my DH was a good father (started dating him when she was 5, she's now almost 30). He took care of her when she was at our house. Not that I didn't do things for her and with her but it was at MY discretion.

Maybe take a step back and leave more to your husband. It's not your job to make sure she has fun things to do on Saturdays. If the Friday night thing is enough for you, then stop at that. She's there to spend time with her father, after all.

Believe me, I was always glad to have my house back on Sundays, so I do get that.

What do you think puts you in such a foul mood by Sunday? Is it spending time with her? Is it that she takes time away from you being with just your DH? I think you need to figure that out.

I never worried about my SD taking my husband's time away from me on the weekends she was here. First of all, he did always want to include me, second, I was fine doing my own thing while they went to the park or whatever (I usually insisted on it).

I know you hope she will be less annoying as she gets older, but my experience is the opposite and the teen years are the worst!

If you wanted to be with someone where it was just the two of you, you married the wrong man. If you want this relationship to work, you need to get to the bottom of your ill feelings towards this girl. And maybe you won't be able to. There's nothing wrong with admitting that you made a mistake and this isn't what you want.

I can tell you from my personal experience that skids do not get less annoying.  Now, I will caveat this by saying that I like my SDs and they're pretty good kids.  But they were less annoying, to me at least, when they were 1 and 4 than they are at just turned-6 and 8.  There are definitely advantages to them being older - they're more independent, they're easier to take places, they can communicate better - but some of those very things make them more annoying, too.  Based on seeing other kids, I'm guessing they'll be even more annoying when they get to be tweens and teens.  So if you're struggling with a 5 year old, it may not get much better with time unless you prefer older children (and it sounds like you prefer no children).

Would it be better if you didn't have to spend time alone with her while your husband works?  If your husband went out with her alone one day of the weekends he has her so you'd have time away from her?  If there were better boundaries, so that she's not ever into your clothes, makeup and skincare products?  (I'd go wild if my SDs ever got into my stuff - they know better than to try).  Or is it just the fact that she's a kid who is with you two weekends a month that is the problem?  If it's the former, talk to your husband about what can be done to make things more bearable for you.  If it's the latter, well, then this is probably not the right relationship for you and you should consider walking away for your sake and theirs.
 

You're putting your all into entertaining her on Fridays and Saturdays and have nothing left to give by Sunday. It would probably help if your DH took her out of your hair all day on Sundays. Is there any family around they could visit? 

You made the choice to marry him.  I get that it is a challenge and I am definitely not playing the " You knew he had a kid and what you were getting into" card.  
 

For your own happiness, move on.  He will always have a kid.  For the rest of his life.

I'm not understanding why you are tasked with entertaining her constantly. This is draining even with ones own children. A 5 year old should be able to entertain themselves for a while - a movie, coloring, legos, etc. It sounds to me like DH has tasked parenting/entertaining this child entirely to you. This child is not your responsibility. You seem to be chafing because your routine is changed. Take some "me time" on these weekends. Go to the gym, out with girlfriends, etc. See how your mood changes. 

Could the fact that you have been through a number of major life changes (marriage, moving...) all the while dealing with a pandemic and craziness of the past year possibly be affecting your ability to deal with sd? That's a lot of stress, then she is one more factor on top of that. She sounds very much like an average little girl. She probably wants to know all about you and wants you to like her, hence the never leaving you alone. Children are seldom really evil or trying to make you miserable. But they are very needy. Until you have to LIVE with a kid, I don't think it's possible to understand how much time and attention they truly need. It's just their nature, 95% of the time. 
Adjusting to your new life and finding the right balance in your new family is hard. Studies have shown it can take an average of 7 years for a step family to stabilize. Of course, that's an average. It might help for you to reflect on all the areas of your life and see where all your energy is being spent. Are there others sources of stress that are draining you? She may be the noisiest stressor but that doesn't mean she's the source of all the negative feelings. Perhaps she's just the straw that broke the camels back.

With so much changing in your life maybe you need some new supports and outlets to stay healthy mentally and emotionally.  It's just a thought. I wish you well.