My children do not have any R with their Dad's new wife. It is totally their choice (they are young adults). But she was the one who broke up the marriage. She was the OW. They both say they will not have a R with her EVER but if he was with someone new - that would be ok.
I do not believe your wife was OW. Have you asked the kids for specifics of "how she treats them" that they do not like? I'd be all over that if it was me rather than assuming they are being manipulated (despite the fact they might be). Step parenting and blending families is NEVER easy. Do you spend one on one time with them without her around? You should.
I feel for you. The whole thing is a mess. But don't lose track of the most important thing - getting shared custody and time with your children. Although YOU don't want to be manipulated - you just gave up time with them. Continue trying no matter what to communicate their importance to you and do whatever it takes to make it happen. I think they are crying out for help in this God awful mess over which they have no control.