The same way you "coordinate" work across your open source dependencies, you post an issue in their issue tracker. As far as those other teams are concerned, you are their customer, and they need to prioritize their work as usual.
If a team is consistently ignoring the issues posted by another and causing issues in the overall project, that's up to higher management to resolve and reprioritize things. Higher-management needs to collaborate and prioritize issues across teams, as their "own" team, since they should have a higher level overview of the project.
To make it a bit more concrete, lets say you have 10 teams of 10 people, each managed by a manager. Each of those teams is an independent "project". The 10 managers themselves form a team that has to ensure those independent projects form a coherent whole by organizing amongst themselves and prioritizing tasks across teams accordingly.
EDIT: this split can work (albeit poorly) at up to 3 levels deep, so ~1000 employees total on a "big project". If you can't make do with that many, you're screwing up somewhere, but 100 should be enough IMO.
If a team is consistently ignoring the issues posted by another and causing issues in the overall project, that's up to higher management to resolve and reprioritize things. Higher-management needs to collaborate and prioritize issues across teams, as their "own" team, since they should have a higher level overview of the project.
To make it a bit more concrete, lets say you have 10 teams of 10 people, each managed by a manager. Each of those teams is an independent "project". The 10 managers themselves form a team that has to ensure those independent projects form a coherent whole by organizing amongst themselves and prioritizing tasks across teams accordingly.
EDIT: this split can work (albeit poorly) at up to 3 levels deep, so ~1000 employees total on a "big project". If you can't make do with that many, you're screwing up somewhere, but 100 should be enough IMO.