For 4 days a month.  If DH doesn’t like it , he can get a bigger home, where she can have her own wing.  It’s guilty DISNEY Daddddy.  

That much is clear. She is acting like a guest, not a family member. Might want to have a discussion with your wife about these things, especially the inequality between treatment of kiddos. This will make your 9 year old resentful over the long haul.

SD is still a teenager with teenager brain and raging hormones. Sounds like there needs to be some boundaries put into place.

Is there a reason she doesnt come over more frequently?

How long have you and your DF been together? If it's a fairly new relationship the Daughter may have a awkward feeling adjusting to Mom being with another woman after seeing Mom being with Dad for so long..... and no, I am not knocking your relationship, just saying it may account for the SD's always staring at you. 

Both you and DF need to take control of your own individual children. Discipline your own, have her discipline hers. If dishes are assigned to your daughter, then you oversee the task and assuring it's completed. Just as picking up after herself and other assigned tasks for the SD should be overseen by her mother. No good ever comes from the stepparent trying to discipline and/or oversee the stepchild if the actual parent isn't on the same page.

I would reclaim your home office space. Something like a daybed could be put in it for the SD to sleep her four nights a month and the rest of the month the room is your space. But during the visitations you should still a a space to escape to. Whether that be your bedroom (and left alone when the door is shut) or you start doing a few things out and by yourself during the times SD visits. Take your daughter out and do some fun things or educations activities. 

Sit down and discuss your expectations with your DF. 

Im confused about gender in this blog. One person called your fiance a Daddeee and another said something about the mother being with another woman. Can you clarify?

If you are a male(although females get accused of things too), I am very concerned for you being around SD. She is over sexualized, watching porn and texting your fiance about her father's sex life ?!?!? Weird. If she is only there 4 days a month, I would stay away. Girls like that accuse people of things that you dont want to be accused of. NEVER be alone with her and be careful of your 9 year old being around her. Be glad it is only 4 days a month but Im telling you right now 4 days a month can change real fast and you can end up like me. I have all 4 skids living here 24/7 because their mother found a boyfriend who didnt want her feral kids around. The younger ones leave 4 days a month for their mother's house. The older ones are too old and never go. Keep reading on this forum. You might just change your mind about marrying someone woth a child like this and dodge a bullet.