Yeah, I believe LILO is the default for Slack but during installation you can specify grub.
Whoops. I totally spaced. I started talking about dual-booting Windows and Slack. You're trying to dual-boot Red Hat and Slack. That's something I've not done yet. I think it's a similar principle, though. You just pretend Red Hat is Windows except for the fact that both can use the same swap easily. So you can partition the new hard drive as all root or subdivide it how you want. Then what I was saying mostly follows: that there's not all that much to figure out. If you get your two drives in and recognized and can boot from CD, you just put the Slack disk in and first thing you do is use fdisk (or cfdisk or something else if you choose) to partition the drives. It's not a snazzy GUI installer but, after partitioning, it's still a menu-system install. Then you tell, well, grub, I guess, to install where you want (I usually do the Linux superblock and flag it as the bootable partition but for this box I put LILO on the MBR - either worked for me) and set it up to boot your Linux from /dev/hdb1 and your other OS from /dev/hda1. Then you go on and install, reboot, and get a menu to load your OSes.
Only thing I'm not entirely clear on is the boot loader issue, like you're asking. I guess you're basically reinstalling the boot loader - replacing the RH grub with the Slack grub and getting a new grub.conf in the process? And then grub loads the kernel from either drive which spawns the init on its drive and runs the scripts in that system. I think that's how it works.