My IC told me that blending a family under the best of circumstances can be very difficult. There has to be a lot of compromise, a lot of patience, and a lot of discussions/communication regarding parenting styles. When a marriage/family exploded because of an A and the two guilty parties try to blend their families together, my IC said that, in her experience, it usually leads to disaster. OW/OM usually don't have a lot of compassion, empathy, or willingness to compromise, which is why they are an OW/OM.
My exwh is not married to the slunt, but they live together now. Her two kids are there more than mine, but are always there on the same weekends as mine. It's not a good situation and I can see it will only get worse as time goes on.
The slunt clearly doesn't really like my kids and doesn't want to acknowledge that my exwh had a life before she waltzed into it. She is very big on making sure that everything is "fair", which means that my kids get no alone time with their dad. They either all do something or they don't do anything during their time together. Since they can't all fit in the same vehicle and it can get expensive for 6 people to eat at a restaurant or go to a movie, they usually don't do much. He spends no real quality time with his own kids and, according to my DD(6), he never even cuddles them anymore.
The two sets of kids also don't get along real well. Her kids tend to make fun of mine and/or exclude them. They are jealous of the other life my kids have had with him and the life that they have with me, just like their disgusting mother. My kids are made to feel like interlopers even though that's their dad's house that he bought. They can't go into the refrigerator to grab a drink on their own or go into the cupboard to get a snack. They get all of her kids' hand me downs, including bikes and bedroom sets. Her kids get the new stuff. She throws birthday parties for her kids, but when my kids are there for one of their birthdays, they are lucky to get a cupcake and a sticker. If her kids happen to not be there, it's even worse. She will go into the bathroom or the bedroom for the entire time and leave my exwh to deal with them. My kids are made to do chores, which is generally okay, but my DS' job is to clean the toilet. To me, that's a massive slap in the face. The kid is there a total of 4 days every month and yet she assigns him to scrub the toilet.
Unfortunately, my exwh is too weak or drunk or stupid to stand up for his own kids. He lets her have all the control, which is what ultimately will lead to the destruction of his relationship with his children.
My point in all of this is this - there is not a lot of love and respect there like there should be when you are dealing with children whose lives have been forever changed by your selfish decisions. There actually has been almost zero "blending". From what I can see, it is a dysfunctional mess that limps along and will continue to do so until one of them cheats. Please know that I mean no disrespect to the people on this board who have blended their families. There is a big difference here - with a blended family that was created out of an A, my experience is that the OW will certainly show her true colors at some point in time. It didn't take the slunt very long; others can put on a show for a while, but in the end, their real personalities emerge and they have about as much regard for the kids as they did for the marriage.
My other point is that there is not one fucking thing you can do about any of this. If the kids aren't being hurt or abused, no court is going to care that they don't get preferential treatment or that their feelings get hurt. You are helpless in having any meaningful control over what happens at the new "blended" house.
However, you are the one who is going to have to teach them how to get along if the situation is less than ideal. You have to show them how to survive because, at least in my case, my kids are in survival mode when they go there. They want to be with their dad, but those other assholes are unfortunately the price of admission. They need to learn how to navigate, how to communicate when necessary, and in what situations to walk away. This is where the fact that you are the sane, reasonable parent becomes critical.