I've been on both ends, so I offer this advice from the heart.
My step-son hated me as he felt that I was replacing his mother, as much as I tried and talked until I was blue in the face, he's just now getting it at the age of 24.
On the other hand, my children love their step-mother and their step-father. (So much so, that my youngest named his son after his step-father).
I was in the same predicament as you and I decided to take the high road, as their father did with my new husband.
I invited the step-mother to lunch at a quiet place, so we would be in a neutral environment. I told her a little about myself and she told me a little about herself. Then, we proceeded to talk about the children. She was so scared of being the "evil stepmother" that she wasn't sure where she stood. I told her that if she were going to be such a big part of my children's lives that I'd like to keep an open relationship with her and discuss the situations with her that arose while the children were at home and would like her to do the same with me. I went over the children's schedules with her, so that she could know more about them. I discussed the good and the bad of the children and told her I preferred to leave the divorce completely out of it. She had nothing to do with the divorce, it wasn't her fault and I didn't want her to feel intimidated around me. I knew she was probably having the same feelings about me as I was about her, and I was right, she was.
We decided to have lunch once a month to discuss the children and that phone calls in between were more than welcome.
When I remarried, I sat my husband and my ex-husband down together and basically we all had the same conversation. We then, all 6 of us, moms, dads, and kids started having dinner together once a month. It was very awkward at first, but my children were worth it.
We grew over the years, to be great friends. My children understood that there was no way they could play the mom against dad (or vice versa) because the lines of communication were open. There were a few disagreements with the ex-husband over the year, but never the step-mother.
My husband and my ex-husband even became fishing buddies. How crazy is that!
My children are now grown men. They are happy, well-adjusted and at holiday times, it's not a mess to figure out who goes where. We all go to the childrens!
Whether you follow my example or not, I know that you're going through a difficult time. Think not of the step-mother as competition, but as an ally, and you'll get through it!
Best wishes and God bless!