At the end of the day, the common interest between a PM and a PMM is to build and grow a product or business. That means a few areas of common grounds:
These questions require collaboration and aligment between PM and PMM. Who takes the lead very much depends on the organization and the strength of the individual.
This is challenging indeed and something I've had to deal with at every company I've worked for. What I've fund helps keep me and the business teams sain is to plan to launch features 14 days after the official planned released date. This makes product nervous most of the time, but most of the time they're also delayed so it all works out in the end.
Goes back to the shared goals - which at a high level, are hard to argue with - revenue, cost savings, customer success, etc. Once you get that common agreement, then it's about the strategy / the "how" to get there. If there are disagreements here, I would start with trying to understand why and seeing it from both of their vantage points. Then trying to see if you can get them 1:1 to understand the other point of view or better yet, get them to talk to each other. Ultimately though if all that doesn't work, you may need to get a tie breaker that's someone else and who they will listen to.