And I want to be Princess of Persia, but we don't always get what we want. She's a parent and she doesn't get to cut out contact with you. That's not how it works when there are kids involved.
Your L sounds like he has a good handle on things, but you seem to be struggling with some appropriate boundaries, still.
You do not need to parent with anyone but your STBXW. You do not need to be calling MIL. Just because MIL will be intermediary doesn't mean you need to allow for intermediaries.
I still believe that there is a plan afoot here to make you get angry/lose your temper and to use that against you, and that playing along and letting STBXW and her family dictate when, how, and with whom communication will happen is a mistake. You get choices, too.
I will tell you again, you should NOT be communicating with anyone in that family by phone or verbally in person, because that puts YOU at risk. People can verbally abuse you, and also play the "What do you mean, you never said that?" and the "I never agreed to that!" games, because there is no record of what happened in verbal communication.
STOP ANSWERING THE PHONE AND STOP PLACING CALLS, because at this point communicating by phone is actively perpetuating the drama, East. You are actively participating in this circus by talking on the phone.
Start sending only emails to STBXW. Everything you need to say about D can be written down and sent to STBXW, and similarly on her end. Stop allowing STBXW triangulate the drama by pulling other people into it whom you then think you have to talk to. If STBXW doesn't want to communicate with you about D exchange, then I guess she doesn't get D (with your L's okay, of course.) If STBXW tries to designate other people, you don't have to play along.
Get written communication written into the custody order if you want some peace in your life in the coming years. Get the custody order as specific is possible so there is no room for arguments. Which holidays go to which parent? What time is the exchange on those holidays? How much vacation time do you each get with her and how does that process work? What happens with extracurricular activities and who pays? If it's 50/50, then require that the parent agree in writing, and if there is no record of written agreement, then there is no need for that parent to pony up 50% of the cost.
This is how you get your independence back, East, and stop being yanked around by the crazy people.
I am sorry that this is happening, but I urge you to look at the reality of what you're dealing with here. An idea that amicable low-drama co-parenting can be crafted out of this chitshow would be naive. Protect yourself with an extremely specific custody order to lower communication and thus lowering opportunities for conflict, because that is what is best for you and for D.