Your feelings are completely normal, and probably very common.
Hopefully though, thinking about your feelings on this thread will help you identify why you feel the way you do, and I'm glad my post might have helped through striking a chord with you.
You do need to get control of how you feel, because if your feelings are leading to arguments between you and you partner than it is causing stress to both of you.
The sad thing about these situations is that for you to feel better about it, the current arrangement that works for your partner, his ex, and most importantly, his children, will have to change. Even if it only changes in a small way. And sadly, that will be detrimental to the other people involved.
If you don't get control of how you feel and either come to terms with things as they are, or get out of the relationship, the ultimate 'losers' will be children. And in your rational, unfeeling head, I'm sure you know that's wrong.
By insisting that things have to change, you are either setting yourself up for more upset if it doesn't change, or something will have to be taken away from people who like things the way they are. Either way, you will end up hurt, because if your partner stops spending time with his children in their own home, there is every chance he will miss is and will start to resent you for causing that. Or, your step children will resent you for causing them to miss out on time with both their parents together, and that won't work out well for you either.
So as lots of posters have already said, you need to decide if you will be happier coping with things staying the way they are for the next few years, or if you would be happier getting out of the relationship.