You arent' doing anything wrong. Her actions are sad, but there is nothing you can do to influence them one way or another.
Your best bet until she is in a place to act as an appropriate mother and adult is to keep your parenting time separate. Explain to them Mommy's nights and Daddy's nights. My daughter was an infant when we split, so I have gone thorugh all the stages. She is 8 now. We are at a place we can be civil and spend a night or 2 a year together for her sake. There was a time that it wasn't the best idea and we just had to explain it to her.
In my opinion, if she is acting this way, I would probably say no on seeing the kids for breakfast. That's just what I would do. If I had nothing planned, I might tell her she could take them for breakfast without you. She does not properly know how to act with you around, clearly. Until she figures that out, you might be better off doing things separately.
You are doing just fine, there is no book on this stuff, and it sure is hard. You are doing great.
