Installed in root, want second in subdirectory

It can be done, I did it here for example:

http://krimsonkloverdev.malbert.me/ – dev site with seperate wordpress install
http://www.malbert.me/ – main site on root level.

I set everything up at my host, I’d recommend you just contact them first and be sure you can have separate database installs as that’s basically all you need.