Mobile redirection to alternate theme

Hello All-
I’m looking for a way to redirect a user from a desktop optimized theme to a mobile optimized theme, or mobile optimized child theme. I know there are plugins that accomplish this. What’s causing me to pull my hair out at the moment is providing a link on the child/alternate theme that allows the user to go back and access the desktop site on their mobile device, if they prefer. This is the key feature I’ve found lacking in the plugins I’ve explored so far.

One option I considered is performing a separate install of WP in another folder on the same server, and redirecting to that folder.

1) Are there any plugins out there that can accomplish this without the bother of another install?

2) Is a secondary install solution a viable one?

3) If the answer to #2 is yes, how do I tie the secondary install to the primary install’s database? Is it just a process of pointing to the primary install’s database in the secondary install’s config.php file?

4) Would the option of the secondary install fall under the heading of a multisite install? I’ve never done a multisite. I’ve read a lot of documentation about it, and this problem seems to fall in a gray area. As in, perhaps a multisite install would be overboard for this particular problem.

Any help would be greatly appreciated!