He told me that it destroys him that I am acting this way

But he's okay with his daughter's total disrespect and name calling? Oh, that's right, you just made that up.

I wouldn't have even said anything to him about not doing anything for her, but now that you have, you don't have to mention it ever again, just disengage and be done.

The blindspot some parents have toward their children is unbelievable.

"He continued to tell me how he doesn't understand how nothing she does makes me happy and nothing she can do will ever change my opinion of her. "

^^^^^^^^^^so after all this time your H is still acting clueless and brushing how you feel and what happened under the rug??? He's not even acknowledging the horrible treatment by his daughter and he's here saying he doesn't understand???

He needs to take his head out the sand and see what the heck is going on around him. Its very concerning how clueless he is and to not understand why you feel the way you do is mind boggling.

"Well DH, it destroys me that you think I WANT this kind of relationship with your daughter and that you think I am lying to you. It destroys me that you think I am untrustworthy. How do you stay married to me if you think I do nothing but lie about your daughter and want to sabotage our familial relationships? Why would you remain married to someone you see as such a horrible person?" Then walk away.

My guess is you'll get crickets. He believes you; he just doesn't want to believe his daughter is that cruel. Turn it back on him and let him explain why he is married to someone who is such a horrible person. That will either force him to acknowledge that his daughter isn't that great or that he truly thinks you're awful. Either way, best to know now than later.

How they never remember their skids bad behavior. Or how the situation went down, and the details are down played. Oh and let's not forget the old, that was a long time ago, why can't you just get over it. I'm sure i have heard every excuse for SDs behavior. Even outright lies to protect his precious poopsie.  

So, essentially he just wants you to take all the crap, say nothing about it, act like it never happens, act like she treats you well and do anything and everything for her. 

Yeah, I can't do that either. 

Sorry he isn't seeing your side of it. How old is she? We just had our breaking point the other day, and my boyfriend is the absolute best, I've really been waiting my whole life for someone so good. His 14 1/2 year old daughter not so much. She's fat, lazy, stupid, rude, incompetent, oblivious, self centered. She's been doing subtle things all along, we have been together for over a year, things were great until fatty mcnuggets decided about 6 months ago that she couldn't cut it with her stepdad at her mom's house either, didnt want to have to help out with her 2 younger sisters and actually told my boyfriend she thought moving here would be "easier", she is the laziest person I think I have ever seen, won't ever even sit up on the couch so everyone else can sit down too & watch tv. She usually does things that she knows make me uncomfortable only when hes not in the room, she won't do it when hes there, it's not his fault he is the best, he does everything he could or should. His idiot daughter cant/won't do anything without being told several times and seems to be completely incapable of learning, it took her 20 times of being told by both him & I not to use MY bath towel, razor or hairbrush and to hang up the wet towel when she was done. I'm surprised this girl even knows how to wipe her own ass,  for all I know she probably isn't doing that correctly, she stinks too. She stats on her phone 24 hours a day, doesn't like books or anything intelligent. I have an 8 year old daughter & I try to do things but with this idiot it's like oil & vinegar, if I'm going right, she will go left, oh wait now I'm going left she wants to go right. She's just disrespectful & I really do believe it's on purpose, this isn't the first family, home or relationship she has wrecked and it seems she didn't want to move back in with daddy until he actually had someone. She sits in my spot, has even tried to push me off my own couch before, inching closer like a little creep hoping I would move. Doing the opposite if what him or I just said, if we're outside she wants to go inside. Day at home, oh she wants to go somewhere, we r all watching a movie, she suggests something else & always asks to change it to her music if we're in the car, and makes fun of the things i like, no matter what it is & makes comments abkut everthing. She's posted an inappropriate video of my daughter saying something online that no kids should be saying right out of the gate, my daughter is much more good & intelligent than her, but every time I turn around I have to reinforce it, we don't do that or don't be like her. I don't even want to try to make nice snacks or anything like that for everyone at holidays or cookout or anything like that because that fat ass will eat the whole thing every time & nobody else gets any, I've tried being subtly obvious, but the idiot doesn't pick up on any hints or social clues either, like if I tell my daughter to throw her trash away in the trash can & clean her mess at the restaurant that obviously means you too, or when you see EVERYONE else getting ready to leave, wouldn't that be a hint that maybe u should get ready 2 go too? Nope, she has to be told more than once & everyone else has 2 end up waiting on her. I don't even want 2 go out 2 eat at any restaurant with her that isn't a buffet. She stares at me the whole time when I'm eating or makes slurping noises at the table when I'm eating my soup and ALWAYS asks to eat off of my plate or my daughter's plate. We went one place and she ate 4 baskets of free nachos, ordered a regular meal then asked me for the rest of my food. She's eaten 40 chicken mcnuggets from McDonald's in one sitting, She sneaks in the kitchen and eats entire containers of things that aren't hers after everyone else has gone to bed. My boyfriend took her to burger king one time and ordered 2 sandwiches & 2 large fries, she thought all the food was for her, he didn't get any, she would eat the walls off the house if she could. I saw her eating the dirt from under her toenails one day! She has to be told to do her homework like a small child and still doesn't do well in school, he can only make her do the work he actually knows about. Her mother is worthless just like her, won't do anything for her at all. She might come up here to visit her for a couple of hours and hang out at my boyfriend's apartment the whole time, or takes her to the mall but never buys anything then brings her back right after. I think she only comes to try & con her daughter out of what little $ she might have. The girl is so dumb she gave it to her to take care of the too many nasty animals they have. The only way we could get her to share some of the burden over this Christmas break was he told her mom that he was bug bombing the apartment & she couldn't be there. He told the stepdad if her mom didn't come pick her up that he was going to drop her & her bag off at their house. He told her to keep her until after Christmas but surprise they don't get along well either & I'm sure she will be back before then. But the last straw was I work hard & I've done a lot for her & I've earned everything I have with no help, I was drinking a beer & she was sitting on face chat on her phone with her friend & mocking me, I waited & checked it to b sure but she would take a drink every time I would & say things like am I bothering you. I slammed my Can down, said we're done! Put my daughter to bed, went in my room & texted him that I didn't want her there anymore. He came inside, told her 2 get her stuff & took her back over 2 his apartment. I don't want 2 lose him but I've been through bad situations in the past & I will not be treated that way ever again. We are keeping 2 different houses until she turns 18, we actually went to look at a house & the things she said then made it clear that she thought it would be her house & she wouldn't do this or that if I didn't want her to, it's really disheartening because I had a job and a car at that age and was out of the house, my boyfriend also had a job & was also out of the house before 18. I'm afraid it's not going to get better, we could really have a lot together if it wasn't for her & at this rate I don't see how this dummy is going to magically turn into an adult in 3 1/2 years. She's making no attempt to get a life here where we live, only meddles in the lives of kids she knew where she used to go to school, an hour and a half away