Im sorry your going through this , and yes being a step parent is super painful most of the time.  Unfortunately like most of us on here ,, this is your life and the way it will continue ,, you need to sit down with your wife and put everything out on the table and be honest with her , have you tried this ?

I truly empathize with your predicament 

Both my ex and I are nurses and he has his son on all our days off. With our line of work, we need our unwinding, destressing time. And guess what? We don't get it. To me, even now that I'm about to move out...it really is a prison like arrangment. There is no time to maintain the relationship, no special moments, no nights out, no having the house all to ourselves. Just making every sacrafice known to man for a kid who isn't mine. 

I ended up realizing I didn't want to live my life that way. But I didn't even like the SS 5, so it was no brainer for me to leave. 

Step parenting it a bunch of cr*p, honestly. No reward but all the work. Hell. On. Earth. 

It won't get easier until SD turns 18, and even then you might have her in your home for a time after that. You have to decide if this arrangment has enough pros to outweigh the cons. I once heard what makes a relationship work is having more good moments than bad. Can you say that about your relationship? Can you make it 7 more years of this? Because it's not going to change even though I know you want it to.... that's a long time. 

Oh boy. Well considering what she's doing to SD's father, be sure to never get her pregnant.  And read a few stories from SMs who are the receiving end of this kind of treatment from the high conflict bio mother of their stepkids. You do realize she'd rather spend her weekends interfering in her ex's life than being with you, right?

Like the crazy exwives who meddle in new relationships and try to dictate the show. It isn't healthy for her to have this much power and dictate when the dad and under what conditions the sd gets to stay with dad

its not healthy for your wife to be this level of controlling. 
 

if the courts haven't stipulated your wife needs to agree on the conditions sd can go be with her dad, and frankly a court giving exwife approval to inspect her exhusbands home is laughable, she shouldn't be involving too much. She has confused concern with overstepping her and others rights and boundaries 

as a couple, you matter too and her placing you as not a priority makes you upset. You can't neglect uour spouse indefinitely till kids are older and expect they'll be waiting happily. We also do not allow skid sleepovers.

my husband is a senior banker and so hometime is our private time and we both don't want stangers staying over

^^^THIS 100percent agree^^^

yikes