then rebooted and was right back into the 3.13 kernel with fat resolution.
It may be that the last kernel that was used was not saved (since your GRUB
was not configured in this way) and, when rebooting for the first time after
the reconfiguration, GRUB chose the latest kernel, i.e., one more reboot
where you would have chosen the 3.10 kernel and everything would have been OK
afterwards. It is just a guess though.
Since I have Fedora 21 and Centos 7 installed on the hard drive also, could I
do grub-update while in either of those to have that grub would handle
bootups after that?
The configuration in the file /etc/default/grub of the system at work would
then be used.
A more important question might be is grub needed in each OS?
You have one single bootloader for the whole computer. It usually is in the
MBR of the disk.