Every Git repository is a separate universe. I mean, even your local repository may be considered as a primary remote repository at any time.
So, how to merge two universes? By force, coercion and fire? Nope, USA is not applicable here, we always lose valuable pieces of work (world) in such a way.
Convention over Git approach is arising here.
First you agree to only sync branches under a naming convention.
You allow to push commits to your side repo freely and automatically until they do not conflict with yours.
If they conflict, another side is free to do, say, a Git-rebase and retry.
CoG deals with and separates notions of Non Fast Forward and Fast Forward commits of Git.
See CoG link, to take it deeper.
To recap, you are in an awkward position with your wishes, because this kind of things is uncommon in the Git world and is not researched well.
That's all. Have questions?