The best thing to do would probably be to submit a support ticket with your hosting provided. They could have done all sorts of things that would cause your environment to differ from a standard Red Hat environment. That said, here's some stuff you could try.
It's possible that the yum directory just isn't your PATH. Since yum is intended to be used by the system administrator it might make sense for it to be in the path for the root user but not for a regular user. So the first thing to try would be running yum as root, e.g.:
sudo yum
If that doesn't work then try enumerating the directories in your PATH:
(IFS=:; for d in ${PATH}; do echo $d; done)
For a regular user I get something like this:
/usr/local/bin
/bin
/usr/bin
/usr/local/sbin
/usr/sbin
/home/username/.local/bin
/home/username/bin
And also for the root user's path:
sudo bash -c 'IFS=:; for d in ${PATH}; do echo $d; done'
And here is what I get for my root user:
/usr/local/sbin
/usr/local/bin
/usr/sbin
/usr/bin
/sbin
/bin
You can check your output against these to see if any directories are missing.
There are also a couple of commands you could use to search the file-system. If you have locate installed you could use that:
updatedb
locate yum
Otherwise, and if the file-system isn't too big, you could use find and not pull any punches (this is probably overkill):
sudo find / -name yum
The same thing goes for the rpm command.
Here are the paths for my yum and rpm commands:
user@host:~$ type -a yum
yum is /bin/yum
yum is /usr/bin/yum
user@host:~$ type -a rpm
rpm is /bin/rpm
rpm is /usr/bin/rpm
If none of that turns anything up then it would seem likely that your hosting provider just doesn't have it installed.
Here is a related link that you might want to skim through:
-bash: yum: command not found