If you are able to boot to your 100 GB installation, which you have already verified by saying you're satisfied with it. Just load Gparted from the repository and remove the 15 GB partition.
If you have data saved on the 15 GB partition back it up.
You don't uninstall Ubuntu (per se), you just delete the unwanted partitions and allocate the space as you see fit.
You can add the unallocated 15 GB to your 100 GB partition by booting to the Live Ubuntu Media and run Gparted from there. It's already installed on the Live Ubuntu install disk.
Resize your 100 GB partition to include the extra space. When Gparted finishes, it will automatically retain the same UUID for the 100 GB partition, which the already installed working grub will see. It's continue to boot to the working Partition.
After you finish the Gparted maintenance, run this command to remove the residue of the previous install (the menu items relating to it in the Grub menu):
$ sudo update-grub