You also seem to be using her as a pawn -- she is HIS daughter as well. Not just yours. Change the "my" to "our". You aren't being accommodating if you make decisions more than just day to day ones without consulting him. If he has joint custody, he gets a say so in the activities, education, and medical of his child. ONE Situation? You are the one who has stated your family has been at war with him since before the child was born. YOU are the one who has stated things about your family. That is much more than ONE situation. That is your family BUTTING IN where they are not welcome and you should make sure they comprehend that.
I'm talking to someone that is NOT my ex. I am talking to people online. To use OUR would imply that myself and the person I am talking to share a child OR that my ex and I are mutually talking to other people. Growing up if I was talking about mom and dad, I would say my mom and my dad to my friends even though they are my and my brother/our parents. My brother was not in the conversation and I wasn't talking to my brother so I properly used "my". My daughter is not a child that you and I mutually share. When I talk to other moms and share stories I would say "why just this morning MY daughter said the funniest thing." It's is normal and proper to use "my" in the situation I am using it.
I'm not making major decisions. My ex and I about a year ago had a situation which did not concern my daughter. In an attempt to get his way he told me that if I do not give him his way then because he has joint decision making I cannot raise my daughter in x faith. I told him I also have joint decision making and disagree. If he wants to make it an issue we can go to mediation over the seperate issue. Then I went back to discussing the situation at hand leaving my daughter out of it. (Because I am tElling the story at hand to you who has no relation to my daughter I am using my again). Actually this particular situation was me mediating a dispute because my ex poked the bear (my parents) and I was resolving THAT dispute. Thankfully they have had no contact since that time. It has helped, but they Def still majorly dislike each other.
But he and I mutually had the child baptised in that faith while we were married, and I continued her upbringing in it. He had 0 issues with it until he needed leverage over me/my parents. He used it before to get his way also, after which I looked up better ways to handle it without him controlling me and thus already had my response prepared.
So I would argue that I am not, in fact, making decisions without him aside from day to day.
Beyond discouraging contact between my ex and my parents to try to minimize the conflict, their mutual attitudes towards each other are beyond my control.