About 10 years ago, I was in your exact.same.situation. My husband's ex was bitter, she resented my coming into their lives as another mother figure, she was still hurting from the separation. She attacked me in our apartment and then tried to run me over with her car, simply because we requested to have the children for trick-or-treat every other year. She refused and it escalated. It was really ugly. She ended up getting a civil protection order against my husband (then fiance) saying he reached into HER car and tried to choke her. It ended up getting thrown out since I and two neighbors were outside and witnessed against her. It was truly an ugly situation.
My advice... Let DP do all of the communicating. Let DP do all the stressing. I know, that sounds hard but honestly, it's not your job. If she wants to be nasty, just don't give her the option. Let them exchange children outside while you are in the house. Trust that your DP is a good father and can handle her. The day I realized that I didn't need to be a part of all of that, a good 3000 pounds was lifted off my shoulders. I just handed it all to DH and let him handle it all. As time went on, she found a new husband and is much, MUCH easier to deal with. I do talk to her on the phone sometimes but for the most part, I still let DH deal with her. My job is simply to love my step-kids and be there for them. DH's job is to deal with her. I didn't marry her, I didn't have kids with her and I didn't chose to have her in my life.... so I don't. DH does great in dealing with her and only tells me what happened if I ask. I try not to. I just ask questions that have to do with the kids, not her.
When it comes to the kids talking about the things she says about us, I pretty much ignore it now. They have learned over the years that I'm just not interested in the things she says. Sure, she says things that make me mad but disputing it to the kids is pointless... they eventually see for themselves what's going on, trust me. As not only a step-parent but a step-child myself, kids DO see who's bad mouthing whom and will respect you in the long run for not being pulled in.
Anyway, it will get easier, I promise. When I was where you are, I almost left my husband because of the anger I felt towards his ex. I almost left because it was SOOOO much to deal with. Granted, we have some HUGE problems with the blended family aspect right now and ex still makes me INCREDIBLY angry sometimes but I have come to a place of zen when I'm dealing with things that come to her. I just always try to put what is best for my SKs first and foremost, it's habit now and after a good dose of angry, I move on and do what I need to do for them.
And one last thing, I will tell you that the turning point in all of this was when I had my own children. The second I got pregnant with my son, I realized that I needed to start looking out for MY new family and stop worrying about HER and letting her rule my life and how I react to her. You can't control other people, you can only control how you react to them.
Good Luck, I feel for you, I really do!