Where's your gumption?  Can't you verbally take out this little bitch?  Slash her with words.  Don't yell.  Don't curse.  But destroy her.  You can do it.  

she knows how to manipulate and lie and act like she is innocent.

Then this is how you treat her in return. She’s a “mean girl.” The more you have your DH half-assedly reprimand her, demand she apologizes to you - the worst it’s going to get. She’ll ramp it up and get away with it, trust me. 

I mean, I don’t think it’s wrong to want to send her home, but it’s not going to fix anything. It will just anger her and create more animosity. Beat this jerk at her own game. You’re older, wiser, and more experienced than her. 

Show her you do not play. 

Few of us have a poster board of "expected behaviors" like SuperNanny, especially in homes with teen and adult skids. You mentioned venting in general about people not cleaning up.  Perhaps you and DH can take a drive together and discuss what type of home life & behavior that you expect.  Keep it general, but speak of courtesy and cleanliness.  Heck, even baboon troops have certain rules...

Pick 5 things that are expected in your home.  All rent-paying adult skids and minor skids should have the situation clarified for them by their father.  Post them prominently.  Seriously.  If they were acting with maturity and consideration this would not be necessary, but ... if they act like little kids ...  Retraining psuedo-adult skids.  You can always loosen the rule

What form of consequence will DH support and enforce?  Yelling or "talking to them" is inadequate at this point. No exceptions and no excuses.  Consequences should support the family unit.  Mowing the lawn, waxing the kitchen floor, painting the garage, dishes for a week, cooking dinners which include vegetables  ... whatever.

Once it is clear what is expected, do not nag, do not complain, merely enforce. 

For instance, we had a problem with personal property left out in the living room.  I tried boxes for each person & nightly we swept the main floor and dumped stuff into boxes if we could identify the owner.  We had mixed results.  

Finally, I started to black trashbag all of SGD's stuff that was left out overnight or when she left after visitation.  Makeup, moldy towels stuffed in the recliner, craft supplies, dirty underwear under the couch, dirty clothes, plates with dried food, mismatched shoes ... everything was put into a black bag and placed into the garage.  The next week, I reminded SO and SGD of the black bag that they needed to sort. Nothing was done until I mentioned that I'd just put it into the trash on Monday.  Light bulb moment for the both of them.  On his own, SO did the black bag thing about 6 months later. SGD became much more accountable for her belongings, her dishes and her trash.  (Okay, hidden dishes were still an issue.)

We all know the passive-aggressive behavior which is driving you mad and it is easy for SO to deny/ignore.  So, get him engaged and involved.  It will be a helluva lot cheaper than a divorce.

Tell your DH if he doesn’t intervene you’re leaving him and keep your word.

Agreed. There’s absolutely no need to address your step children’s sexuality in a derogatory manner. Plus, their sexual orientation is irrelevant here.  

The clinical history of the word "homosexual," is aggressively used by anti-gay extremists to suggest that gay people are somehow diseased or psychologically/emotionally disordered.

The more you know (insert rainbow emoji). 

I'm gonna give OP a pass on the orientation comment. She's under the gun with I don't know how many skids and clearly it's not going well. Maybe the mouthy kids have her saying and thinking things she might not normally say or think. I GET THIS! Only she knows if she has a problem with their orientation that preceded them moving in. If so, that's for a different post, but I'm giving her the benefit of the doubt because I don't know.

That aside, yea, some of these posters are right. You need to take back control. The kids are mean girling you -- the "stinks" comments sound so much like something my two "best friends" pulled on me in college. I was baffled why these girls were suddenly harassing me and writing "Tide" on my door. (I'd borrowed a sweater and returned it without washing it because I ended up not wearing it -- and THIS was the infraction that turned my "best friends" against me.) This stuff will make you crazy and it reduces us to junior-high hurt if it's not managed.

Fed, you don't say how you got along with the boys before SD came for the summer. It might be helpful to know if SD is driving the bullying or if there are always problems with the SSs too, but maybe without the mean-girl dynamic ???

If it's SD driving it, just deal with her. Take out the queen bee and the hive will collapse. Besides, you live with SSs full time, so best to deal with their bad behavior after the queen is gone.

Here's some validation of what you're going through:   http://www.stepdigest.com/2015/10/26/relational-aggression/

Read up on relational aggression and different ways to deal with it. You just have to get through this visit. Then you can put down your foot for any future SD visits. After a quick scan, I don't see a lot of ways to deal with it hands on. Best to avoid her now and in the future.

Whatever you do, don't let her see that she's getting to you. Leave the house, take a trip, spend weekends away, get your husband to take his tribe camping or on a trip...whatever you have to do, do it. Once SD gets a taste of blood, you're sunk. And if she sees she's causing trouble with you and your husband, you're sunk.

Don't make any decisions now about divorcing. Wait until she's gone and then see if your husband is willing to go to her if he's so interested in seeing her (doesn't sound like he is). Try to be measured when you talk to him about this -- even though he doesn't seem to have much regard for SD, he'll still likely be defensive if you come on too strong. Just say, "I'm not willing to have a repeat of this summer so you need to make other plans regarding SD" and see where the discussion goes.

SD is running wild with power this summer -- probably because she knows she's getting a rise out of you and she knows she's not going to be there for long. She's trying to make the most upheaval in the time she has. Leave the dirty dishes, leave the trash -- just be hands off until she's gone -- then tackle the issue with your husband when she's not there to defend herself.

Good luck. I know how hard the mean girl stuff is. I have a mean girl SD too and she's not allowed in my house. That really took her power away.

You need to stop having verbal confrontations with her and get passive agressive.  She leaves stuff laying around? Make it dissappear.  She won't wash her dishes, then she only gets paper plates and cups, etc.  

There is no need to have any conversations with her.

Stop attacking this SM. She's at her wit's end with an obviously defiant SD who has no respect for her. She deserves to rant! Lay it all out there. Sexual orientation, weight, everything is fair game! I'm sure skids are having a ball attacking her from every direction. Sounds like she lives in a house where skids judge everything she does. I would say leave that situation because it's clearly not safe for you. Take care of yourself and your well being. 

Your house, your rules. I commented something similar on another post. Disrespecting you is disrespecting the home. Disrespect the home, you can leave. Your DH and you must be on the same page. Sounds like your SSs are young adults and old enough to get their own place. If your SD is going to disrespect you... DH needs to spend his time with her elsewhere. You and SD don’t need to be friends, but under your roof that you help pay for... I wouldn’t tolerate that abuse.