Child theme in separate WordPress Install

Apparently what you want has been discussed for seven years now and still is waiting for a final solution.

However, since 4.7 there is the function get_parent_theme_file_path, which is called when a parent theme file is needed. This function has a filter which allows you to change the location. So, if you insert that filter into your child theme, you should be able to redirect all requests for a parent theme file to another WP installation altogether (if the security settings on the parent install allow outside calls to individual theme files).

I haven’t actually tried this, but it should work.