I need someone te hear me out so I know I’m not over reacting

So my man has a daughter who I met when she was 3. She’s 8 now and since I’ve met her, her mom has always made it difficult for us to see her. She takes her when she feels like she’s doing good and then when she isn’t stable enough she wants us to pick her up. (In a whole other state btw) which we gladly do however she’s moved back and forth between states so much that she has not spent a full year in a school since kindergarten. This last time her mom asked us to pick her up because she was sleeping on her car with her. We did. And kept her herein school until the school year was over. It was decided that she would spend the school year with us and summers with her mom. Well as soon as her mom got her back she blocked my man won’t answer calls we don’t have an address we don’t have the numbers of the boyfriend or mom of the boyfriend (who’s taking care of her when her mom is not around.) this is not the first time she’s done this. Basically every time she goes back to her moms we don’t know when we will see her again. Which brings me to my issue. I am tired of this. My man as well I see how it takes a toll on him. However he does not want to go to court and open up a custody case. I ask him why and he says because he knows eventually his ex is going to call again and our daughter will be back with us again. I don’t feel like that’s the right way to do things or the right mindset. As my stepdaughter has gotten older especially this time around I’m noticing how all the change and moving back and forth is affecting her. She cried because she didn’t want to leave us and even those first couple weeks where we call her on the phone she wanted to come back. We now have no contact with her until her mom decides she wants to let us and I just can’t believe he’s not trying harder for her. He won’t try to call her mom ( I have her number on my phone she hasn’t blocked me only him) unless I bring it up. Like I’d be calling every day and bugging her. His ex can be really unreasonable but still that would not deter me from wanting to know when I’m going to see my child again. Am I wrong here? Should I let it go and let him do things his way? Which is basically so nothing until she decides to call us again for help. Idk this is really turning me off to him.