Here's what I'd like:
REPO-A
/.git
/otherFiles
/REPO-B
/.git
/moreFiles
I want to be able to push all of REPO-A's contents to REMOTE-A and only REPO-B to REMOTE-B.
Possible?
It sounds like you want to use Git submodules.
Git addresses this issue using submodules. Submodules allow you to keep a Git repository as a subdirectory of another Git repository. This lets you clone another repository into your project and keep your commits separate.