What I had to contend with was slightly different -- AXH was actively trying to put a wedge between me and the kids by saying bad things about me when the kids were in his care. My approach was to focus on telling them the truth when they were with me. I never cheated on your father. I will never be angry with you if you come to me with things he has said and ask me if they're true. Etc.
For me, it was another one of those things I could not control. Like I couldn't control if he made sure they had lunches when they were staying with him. Or like I couldn't control if he made sure they went to bed at a decent time.
My therapist kept telling me that the only thing I had control over was MY relationship with the kids, and how WE interacted. And that creating a healthy home and showing them I love them is the best way to provide them with a model of what a good relationship looks like.
She said "You can't make him behave towards them like you'd like him to. You spent 20 years trying to make him behave like you wanted him to. How'd that work out for you?"
Ditto. I have no control over their relationships with their dads. I battled with my son's dad for a long time, arguing over whether it was okay for him to probe my son for evidence I was abusing him or neglecting him, arguing over whether it was okay to tell my son to keep secrets from me. I argued with him over little things about whether or not some of his parenting choices were appropriate, and why he did this or that. There was never any cooperation between our households. Eventually I came to realize there never really would be. Some of my complaints were a clash in parenting styles -- some of them were 100% legitimate concerns that were never addressed. It created a lot of anxiety in me. It was a waste of my time, and at times it made me look and behave unacceptably.
Parenting is a long game and it takes a long view. You just do the right thing, whatever that is, and know that eventually your children will respect your ability to remain steady and manage your business while the other party(ies) flailed around making excuses for why the child's best interest took a backseat to their denial and manipulation.