HELP Co-parent questions a long emotional roller coaster

I'm looking for advice and really want to know if I'm in the wrong or if there is something I can do to better the situation. Just to give a little background. My ex and I have a very active no sit still for any reason 14 month old. We broke up when she was about 8months We lived together until our lease was up, this was after her first birthday. I moved to live closer to my family and he moved in with his new girlfriend. Yes he was dating her while we lived together, they started dating a week after her birthday party. One of the many reasons I wanted to end the relationship was because he seemed to always prioritize other things over me and our daughter. The whole year we lived together he never took care of her alone or took her any where just the two of them. And not because I didn't allow it, it was him that had reasons why he couldn't do it. Now that we no longer live together he wants me to leave her with him all day or at least most of the day at what ever meeting place we pick for that weekend. Since we agreed she was not sleeping over nights during the weekend at his girlfriend's, because our daughter does not sleep in her own bed nor does she sleep thru the night. Not to mention it is not his apartment. The agreement was that I would drive closer to him two days a month, and he would drive closer to me the two days. Making it so he can see her at least one day a week. The first weekend we scheduled this I suggested we meet on friday a day that I was already going to be close to him because the original day Sunday would mean we both would have to drive an hour to meet. Meaning on Friday, he would only have a 20 min drive, and I would have 1 hour and 45min drive.  The location had lots for them to do, so there was no reason to leave and this seemed to be the better option. We literally argued on the phone up to the point it was time to meet. So I asked my mom to step in and bring our daughter to him, to give me time to cool off, and so he didn't have to worry about her wanting to be with me and not him. She is not in daycare and is with me all day so she can have attachment issues. My mom did and she stayed in the area where they met just in case our kid needed something, since because he has never taken care of her alone for no more than hour or two and that was only in our apartment. Not to mention, it would make the hand off back to my mom easy, so we didn't have to play phone tag since the place we were was huge. Now he argues that his visits are supervised and that it is not fair to him. My mom sat nearby and was on her phone most of the visit, only stepping in to suggest things they could do since all he did was hold her until she started fussing. He didn't offer her to play in the kids' area or go on any of the rides. My mom could clearly see our daughter was getting upset, just being forced to sit next to him. He then left early. I made sure i planned for them to have at least two hours together. He left after about an hour of his own choice. A few days later, we started to discuss the next meeting location. I suggested a mall close to me that would be about 20 mins for me and a 1hr and 45mins for him. Plus I had to work that day. He argued it was not fair for him to drive all that way to only get an hour with her. I always plan for the two of them to have at least 2 to 3 hrs together. He doesnt want to acknowledge thats about all the time he would spend with her when we lived together. And that last weekend was only planed because I had something to do and was not planned with him in mind. I cave and suggested a place that was 40 mins away and making his drive a little less. Because I had to work. I had to ask my mom to take her. With this move money has been tight so since my mom was giving up her Sunday, I gave her gas, toll, lunch and spending money. Money I really didn't have. Ex ended up going to the wrong location that was an hour away from them. He is pissed and tries to make it partly my fault because I didn't pick up the phone when he called to say he was running late. And when we did talk we argued because I said I wasn't going to be the go between him and my mother. He can call her to see where they are in the mall and that because he was late that they might be eating lunch by the time he gets there is not fair to him. I tried to explain that if our kid is hungry why would I force her to wait to eat then she is too frustrated to eat because now she is hungry. And I don't want her filling up on a bunch of junk food. Am I wrong for not wanting to just leave my daughter with someone I can't confidently believe that can take care of her? He says I'm keeping her away from him. But I have been trying to make sure they can see each other at least once a week for a few hours and that she video chats him every night before bed. Her bed time is 9pm every night. He calls some how manages to always be at the gym at that time or calls 30 to 40 mins later when she is just about to fall asleep. What else am I supposed to do?