I'm suggesting you do this to test and figure out where things are going wrong.
The plugin WP Hide Dashboard happens to work by hiding links for Subscribers. When people login at http://example.com/wp-login.php they are logging in on the MAIN site. On that site, your sub-site admins are, logically, subscribers. If they logged in at http://mysiteurl/subsite1/wp-login.php then they SHOULD go to http://mysiteurl/subsite1/wp-admin however...
I use that plugin and wp-admin is still available. For everyone. There's really no harm letting people login via wp-admin. All that generally happens is you get this URL:
Which says 'After logging in at domain.com/wp-login.php, we'll kick you to wp-admin.' If I login as a regular subscriber via wp-admin, it sends me to my profile.
You're going to have to do some testing. Turn plugins on and off. Turn customizations on and off. Figure out WHAT exactly is causing redirects and what isn't. IIRC your site has a metric ton of weird customization and command duplication to fit your needs. You can't reasonably expect all plugins to work correctly when you do that. In fact, I'm pretty comfortable suggesting that you've got a conflict in one of your other plugins/customizations.