Don't date horrible men who train their kids to lie by giving them positive attention when they do. From your post history, you got mixed up in an unusually bad situation with an unusually bad partner and stayed too long. It makes you question your judgement and your worth. What you describe happens with more frequency to people on this site than the general population, because we all come here due to having problems. But it is NOT normal amd you should bolt at the first sign of it in any future relationships. 

I have never felt this.  I would never tolerate a relationship where I would feel this way.

So, my answer is.. I would not deal with it. I would boot the POS child worshipping parent and their lying pelvic projectile to the curb and out of my life.

Life is too short to tolerate toxic.

I couldn't be in a relationship where my partner didn't believe what I told him.  

There was a moment, fairly early in our relationship, when I got mad at one of DH's kids for destroying something of mine and DH got mad at me over it. I didn't yell at the kid, but I was visibly upset and the kid cried to DH. DH was upset with me and I reminded him that I didn't yell at his kid and that his kid was in the wrong. The kid was 10, not 2, so should have known better, but still is pretty immature for his age. That was a turning point for me and I thought about ending the relationship. It hasn't happened again, but there are still times when SSs are rude, disrespectful, or damage things and DH says nothing. I know he wouldn't tell me to leave over his kids, but I still believe that stepparenting is a completely unnatural situation and is challenging if your DH hasn't decided that your relationship is just as valid as any other romantic relationship, it's not secondary to his children. If everything becomes a struggle over the kids being right and you being wrong, then your DH should never have gotten remarried. 

I couldn't be in a relationship where SO would side with a child over me. That would say to me that SO doesn't trust me to be honest and sincere. If there isn't trust then there is no relationship.

I had a talk with DS once, he asked me a very deep question.  So I explained to him that I will always love him most. But, some day he is going to grow up, leave, and start a family of his own. If he loves me back he would want me to be with someone who treats me well and I can be with so I am not alone.

I don't think it's about the SO choosing their child over you, BUT if your SO can't believe or trust you, seems like that's the problem. Makes no sense why you'd lie..

My step daughter used to lie and deny all the time. I finally told him that if he thought I was such a horrible person that i would lie about what she was doing to get her in trouble for no reason, then we needed to break up. He had a moment of reckoning there and stopped believing her.

At the same time, I stopped handling her discipline and her issues altogether if he's not around. If he's here and she does something, I'll inform him and let him deal with it. If he's not here, and it's not a major infraction, I ignore it.

Like, earlier, he told her to take a shower and my son to do the dishes. When they were BOTH done, they could play Xbox. She waited a super long time to take a shower, but she was done before my son finished washing dishes and she got on the Xbox anyway. I'm not going to police that, it's not worth the stress. If he were here, I may have said something to him.

I'm not sure how to deal with the insecurity but I definitely feel it. 

That said, a few months ago, she created a ton of drama and was awful to my kids. It was to the point that my husband was ready to stop bringing her here to the house. I don't want that and he doesn't want that. But at least now I know that he won't allow her to hurt innocent people (us) for no reason.

THIS 

At the same time, I stopped handling her discipline and her issues altogether if he's not around. If he's here and she does something, I'll inform him and let him deal with it. If he's not here, and it's not a major infraction, I ignore it.

I don't let an opportunity even arise with SD. I have disengaged. I can't "inform DH she didn't do her chores" if that is HIS responsibility. I have let DH know he is the parent and needs to do such things. I used to try to handle some parenting things, but it ended up being confrontational. So much less stress knowing it's not my problem anymore. 

The way to deal with it is to find a man that knows how to treat a SO like an SO, a child like a child, and an ex- like an ex-.  You and your BF’s kids are not on some sort of level playing field.  You are his SO and should be treated as such.  His children should be treated like children.  In other words, your BF should realize that kids, being kids, can be very sweet, yet lie, manipulate, etc.  It is all part of being a normal child.  Instead, what your BF has done is set you up for insecurities and failure.  He did this by giving his children the power to manipulate him.  They are quickly learning, all they have to do is whine and point at you, and he’ll buy it.

Again, the way to deal with it is to find a man that knows how to treat a SO like an SO, a child like a child, and an ex- like an ex-.  Your current BF doesn’t sound like this type of man.  He sounds like the type of man who wants to make things as easy as possible for himself.  It is easier to just pander to kids than actually be a parent and discipline them if need be.

You are much better off by yourself (not alone, but by yourself) than you are with a man like this.  Far too many men out there with children think that this gives them a license to do what they want, while their “little woman” is supposed to suck it up and take it or make it somehow work when she is being set up for failure to begin with.

I know what you mean and unfortunately, I don't have an answer for you. I've been with my husband for 5 years now (married 2) and I still have that in the back of my mind - that when it came down to it he would choose his daughter over me. I think a lot of it is our society and how you constantly see comments from parents saying their children come first, are the most important thing in their lives, etc. I desperately want children of my own but so far, it hasn't happened. So here I am with the most important person in my life being my husband and the most important person (based on what so many parents say in forums - I would never ask my husband how he felt) in my husband's life, his daughter. It doesn't seem right. I don't think it's supposed to be that way. I hope I don't get judged too harshly for saying that. I'm not trying to stir stuff up. I'm really sorry you're feeling that way. It's a horrible feeling.  I guess for the most part I just try to pretend it's not there.