It's understandable that you want the best for your sons, especially with their relationship with their father. And if you were married or significant others, looking out for their father's emotional wellbeing is absolutely the right thing.
Another one of the hardest aspects of divorce is letting the kids and other parent create their OWN relationship. It will be very different than what you would want it to be.
The kids had their boundaries, they knew what worked for them. Respect that. Their dad called the kids on the wrong day. YOU got upset that he was feeling mopey and pushed to fix it. The 'softie' son who was perfectly fine with not talking to his dad was pushed TOO do it. What does that teach him?
I know this sounds rough. This is a painful learning curve. Yet with each owie comes an opportunity for growth. The trail is rough now full of pitfalls, detours and barely visible.
Keep going forward, pushing through. The more you're able to divorce yourself emotionally the better you can move forward.
Cry, get mad, process the hurt, betrayal, agony, sense of helplessness. Turn to a friend who listens. Find a great counselor.. they can make a world of difference.
This was about you, not him. You are not their dad's emotional confidant. You don't know, nor is it your responsibility to know how he feels, what he needs. He's turned to someone else. And she is working to create an integrated relationship with him and the kids. Her texts are not directed to you. They're giving feedback on continuing a relationship with him and trusting her.
Is what he did to you fair? No. Is how he went about it wrong? Yes.
His actions speak louder than words. Let go of the connection you once had, want to have. I still perk up like a puppy when the former spouse asks me to work on resolving something together. Why? Because I felt we were always such a good team. That part always made me feel good. And I just go there.. and THEN get upset I went there. He didn't do it to get to me. I did.
You are doing great, even if it feels the opposite. Respect your children's choices when it comes to their dad. Toss yourself some extra love.