It's best for the kids if things are not contentious at all. You are the mom and you need to be confident in that. It's great that you are not jealous of her and I'm sure that will come across to her. She's probably nervous as well. I would take the position that you are so happy for them (even if you couldn't care less!) and that you feel that a happy home situation on both ends is essential for the girls. If you welcome her into their lives, there hopefully won't be a competition.
My husband's ex was always so jealous and really mean about visitation. Constantly interfering, reinterpreting the agreement, and so on. We even had to reschedule our wedding (planned for "our" weekend) because she decided to mess with the agreement. So it caused a lot of problems. If you and your ex can get along, be flexible when necessary, and accommodate the kids' schedules, that will be great. If you can manage to invite both your ex and his wife to the kids' events (games, concerts, etc.), that's a good start.
If you can let her know that it takes a village to raise a child, and you welcome her involvement, great. You and your ex are still "the village elders" and call the shots - let her know that you appreciate your ex's willingness to work together with you up to this point, and you welcome her to join in on that system already working. I don't think you need to consult with her on things, but you do need to be prepared for the fact that the kids may ask her stuff or go to her first on some occasions. For example, my stepdaughter was with us when she got her first period - so I had to deal with it and unfortunately the mom wasn't the one who had that "privilege" - irked her to no end, but what could I do?
If the new wife is secure in the fact that you and your ex have a sort of shorthand between you after being married 22 years, great. If she knows that you are secure in the divorce and in your new life, even better. If you can let her know that you think the more positive role models of the same gender in the life of 2 girls, the better - outstanding. I'm not sure how old the girls are, but the more you can be allied when they go through the teen rebellion and hormone thing, the better off everyone will be.
If it's been 10 months, this new wife probably hasn't known your husband all that long. You might start by gentling inquiring about HER life and interests, and any nerves she might have about "instant family" and offer to be of help there. That's a good starting point, and then you can offer some of your own opinions/values.