I got your rude private message.
The thing is, it really does look like you're looking for help here and you really don't understand this dynamic, but I feel like you are a chasm away and you won't agree with/even really understand my perspective.
It sounds like when you came into their lives, they were decently comfortable. Not perfect, but they had worked out a routine and a family pattern that worked. The girl had the mother's attention in the evening, and the boy had a lot of freedom to enjoy the TV in the living room and vent steam from his day - having ADHD and taking meds causes a lot of mood swings and difficult social problems, and his days are probably pretty prickly and difficult. Before, he was given a lot of slack.
Now with you there, you've taken up a lot of the mother's time from the girl, and the mother is now pregnant, and you're taken the freedom and man of the house freedom from the boy. Both have suffered losses. And it is pretty clear to the boy you don't like him (probably few adults, and extremely few male adults act in a positive way toward this child) and you are one more disapproving adult and worse you are living in his home changing the tv channel and disciplining him.
And now, to make matters absolutely unworkable, you two have created a baby and now you can't leave now that this is really a very very difficult living situation. You are stuck. And I do understand in this whole picture, you've suffered too. You are now stuck in a situation where you are very unhappy with the children who live there, although you still want the woman and baby.
The girl will outgrow this. In a few years she won't want to be around her mother. Although honestly, the clingy very loving behavior may be replaced by something worse.
The boy won't outgrow this. He will have harder and harder challenges as late teen years come on, and your dislike of him will intensive and his anger that you are in the home will also intensify.
The mother will become more and more exhausted - she will have a 3rd child to care for, and the stresses that her oldest son once caused her will multiply as he becomes more difficult as a reaction to your presence, and your pressure increases on her to make him behave, an impossible task. Looking into her future, I wouldn't want to be her.
The only thing you can do here to change this is to change your attitude about the children. Pretend to like them. Just pretend. Say nice things about them - hey I saw you got an 80 in math, great. Whatever you can think of that's positive, say it and mean it.
Right now, you only represent a loss to them. You may react with feelings like kids should always be respectful, etc., but that doesn't help.
If you actually want to IMPROVE THE HOMELIFE, just walk around acting like you like them. That's your only role anyway, you aren't their father and they resent you.
I see the courtroom in her future too, help, but it's divorce court. And then she'll be with some other guy who doesn't like her two children, and doesn't like yours either.
And that's honestly good advice. Take it or leave it - if you take it, in two years your home life will be tolerable. If you continue like this, it will be hell.
Maybe you should refer to your below bottom posts. Pretty much the same advice. Sorry you don't like her kids. You knew that ahead of time.