There is currently no way to limit sharing to only a portion of the family tree.
You could maintain several family trees for each of the branches. You would have access to your whole family tree with everyone's information, and when you update that tree, you would also have to update one other tree.
Or you could maintain one additional family tree that only includes information that you don't think people would mind being shared.
One thing to keep in mind is that there is no way to unshare a family tree. Even if you delete the tree, anyone with whom you have shared the family tree will still be able to access it.