Proxying a subdirectory to a remote site
Drupal should be able to install into a sub-directory and "just work" without fiddling around with it. This question already answers this particular sub-directory issue:

How to get Drupal 7 installed in a sub-folder / sub-directory properly?

Try re-installing a fresh installation into the sub-directory. Can you login? The .htaccess of 2.site.com should have nothing to do with the issue at hand regarding 1.site.com.

The reason for your problem is likely something along the lines of a clean-url issue fighting against your configurations. A fresh install will be the easiest way to resolve this particular issue.

Regarding this line:


  and I'd like only that subdirectory to go to an arbitrarily named
  server with a drupal install at, say "https://2.site.com"


The domain merely points to a directory. The domain ISN'T an actual file location. As such, this particular line doesn't seem to make any sense. If the issue is not resolved by simply clearing out and reinstalling Drupal in the sub-directory at hand, please re-state your question by providing more information, describe where these sub-directories are in the system root relative to each other and then describe which directory each domain points to. Don't describe domains AS directories because they aren't directories - they're pointers.