Network theme login box on home page

Hi - I'm in the early stages of building a multisite site based around the network theme. One thing I've immediately noticed that I believe will be confusing to new users is the login box on the main site. When they enter their login details, the system tries to log them into the dashboard of the main site (which they don't have permissions for) rather than into the dashboard of their site.

My question is - is their any way to change the login box so it automatically redirects a user to their own site's dashboard rather than attempting to log them into the main site and coming up with the resulting error message? Just trying to make it as user friendly as possible for non-wp savvy new users!