How can I set up another copy of Coppermine on the same server so my daughter can have a seperate gallery?
You install it the way you did the first time, except in a different folder, and use a different table prefix if you want to use the same mysql database. If you can spare another database, set up the installation as if you're starting from scratch by creating the db and user and follow the rest of the coppermine installations.
Is it also possible to run two galleries on ONE installation in the same folder?
Not in any way that would be practical. What are you trying to accomplish ?