I'm in a very similar boat. My H is determined to be extremely involved in my kids' lives. Since he is an outstanding father, I am grateful for this.
But I do not place the calls. If D2 asks to call, then I hand her the phone. H programmed his phone number into our speed dial, so she even knows how to dial. She rarely asks. Other than that, H does both his daily calls, and has to be aware to call at an appropriate time when he can "catch" us. If he is late with his call, then there's a good chance he'll miss us. He's learned that the hard way, and found that to be a tough consequence and I can now set my watch by him
If he wants extra time with the kids, I happily will agree to it. If we already have plans then I express my dismay that "it just won't work".
This leaves him to bear responsibility and live with consequences if he flakes. And none of it falls on my shoulders to manage. I just sit back and behave as honestly (and busily) as possible.