The path of least resistance might be just to run your software in a docker or LXC. But the simplest way I know to get this to work in a chroot is to set up a filesystem with an entire working linux distribution. So here's how to copy your entire existing OS into a /chroot directory and then you can do in the chroot pretty much anything you could do with the base system.
I don't have a RHEL system lying around, so this instructions were tested on CentOS 7.
run all of these as root:
Move to the root directory
cd /
Create a chroot directory
mkdir chroot
Copy most of the operating system
cp {bin,etc,lib,lib64,sbin,usr} /chroot/ -a
Make placeholders for the rest
mkdir /chroot/{root,dev,home,mnt,opt,proc,run,sys,tmp,var}
mount the special filesystems to your chroot
mount -o bind /run /chroot/run/
mount -o bind /proc /chroot/proc/
mount -o bind /sys /chroot/sys/
mount -o bind /dev /chroot/dev/
Enter the chroot
chroot chroot
Since we didn't copy /var or /run, yum won't be able to resolve the $releasever and $basearch variables, so we hard code them into the repo file. This is the path to the CentOS repo, you should change this to whatever Red Hat uses. S you might replace CentOS-Base.repo with RedHat-Base.repo or whatever is your base repository in the /etc/yum.repos.d/ directory. ALso, make sure the architecture matches, this instruction is for 64-bit x86, which is most likely what your using, but if you have a PowerPC server or something really strange, then modify accordingly.
sed s/\$basearch/x86_64/g /etc/yum.repos.d/CentOS-Base.repo -i
sed s/\$releasever/7/g /etc/yum.repos.d/CentOS-Base.repo -i
Now you can invoke yum and install software
yum intall vim
This will install vim in your chroot but not your base system. For hardening, you might want to go through and remove a bunch of packages from your chroot, as this is pretty much a full fledged Red Hat server running in the chroot at this point.