Well, you need to install redhat, but first backup the /etc/lilo.conf from your mandrake install.
The / thing will not effect one or the other, as you will be installing / as a mount point for redhat on this partition or hard drive (seperate hard drives are easier.) than anything else. Let redhat do the defaults, then change them how you need. You will see how you want it. MAKE SURE IT DOES NOT FORMAT ANY CURRENT LINUX OR WINDOWS PARTITIONS, as it will rm -rf all of your system after you pick the packages to install. Also, you can choose how you login with redhat after you get the packages installed. Its where you choose your window manager. I would go with command line, and not with gui, because it could dye hard on you. Also, make a boot disk, you may need it later when you start editing /etc/lilo.conf
You will need to make a decision, will mandrakes bootloader be the one I want, or is redhats. I personally like redhats lilo.conf over mandrakes, but it's up to you.
there is more on this at
www.linuxdoc.org