No we are not married. We do not intend to get married because of different issues. The girls know that and tell us that they do not want us to get married nor do they want their mom to get married. I have been the one and only girlfriend he has had, as she has had one boyfriend (fiance) for the last 4 years. We are commited to one another as mom is with her fiance. She has been "engaged" since before the divorce was finalized and has no plans as far as we know to marry. I in now way want to be their mother. they have one. I do not want to take her place, children need their mother as well as their father. She is reassured of tis every time the argument comes out and she claims that she doesn't feel that way. i enjoy spending time with them. i also don't want father to lose time with the children because mom feels some kind of way of me taking them out.
Just because we are not married does not mean we are not family. just as her and her fiance are not family. they are family, we are all family. I also would feel that way if roles were reversed, it is only human and probably a mother instinct. I could see if I was new and father had tons of girlfriends since the breakup of the marriage but 4 years later this comes up. it is also like father does not spend time with children, as she takes it.
i just wanted to see if I am wrong in feeling that i can take these children out with me, especially if they ask to go. i enjoy the time that they are with us and miss them when they are gone, does that make me such a horrible person or does that make my boyfriend horrible for his life partner, as we call each other, to spend time with his children.

I am in a similar situation to yours. We tried the route you are on and the bio-mom just got more and more bent out of shape and took it out on the boys. So, we have taken a different route and it is working better: Dad nearly always picks up and drops the children off by himself. (He still does not go into her house which bothers her, but he refuses to give in on that point as he feels since he is married to me, not her, there is no reason to go in.) He spends equal time by himself with the boys, and with the boys and me. The boys now very, very seldom do anything with me without Dad. It was an adjustment, but is well worth not having the contention. The boys are much happier now that their mother does not have as much to complain about. Hope this helps!

thanks for all your comments and advice. I really do not care what bio mom thinks. Father and me are very good to those kids and that is all that matters to us. What I was really looking for was if bio mom had a right to say what dad can and cannot do when it is his time with children.

Like it or not, and hard on you is that they are still a family - divorce doesn't divorce the kids from the parents. The best thing that you can do is talk to the dad. He needs to approach the mom and work out better co-parenting. Your relationship with the girls is hurting them because dad isn't supporting mom's relationship with the girls. The same rules need to apply at both homes. If dad won't do it, then you can try to approach mom and work something out. It smells like to me that the girls are in avoidance mode with mom - it's really important to find out why. Then you can move forward intelligently.

Stepmothers/fathers should have some sort of respect because they are also leaving with you and taking care of the children. Taking to much control can probably result in family issues though, especially in the teen years.