Creating a partition in unallocated space
The empty space is on disk2 right behind your FAT32 partition (index number 4) with the start block 1563172864 and the size 390352270 blocks (visible in your sudo gpt -r show disk2 output right at the beginning of your listings).
First backup all your volumes.
To create a new volume with gpt boot from a different disk (e.g. disk0s2/disk1: "Macintosh HD").
After booting open Terminal.app.
Enter diskutil list to get an overview.
Then identify the DiskIdentifier (e.g disk2) of the disk you want to add a volume to and enter sudo gpt -r show /dev/disk2 to get the partition table of disk2.
Unmount all disks related to disk2. This is disk2 itself and any inlying and mounted CoreStorage volume (e.g. disk3 aka "Mac Backup 2") on this disk:
diskutil umountDisk /dev/disk3diskutil umountDisk /dev/disk2
To create a new partition enter:
sudo gpt add -b StartBlock -i IndexNumber -s SizeInBlocks -t GUIDType /dev/disk2
StartBlock is the number of the first block in the unallocated space and NumberOfBlocks is the number of free blocks or smaller. NumberOfBlocks has to be dividable through 8!. As IndexNumber use (biggest index number already there + 1). Then enter a GUIDType.
One valid command would be:
sudo gpt add -b 1563172864 -i 5 -s 390352264 -t 48465300-0000-11AA-AA11-00306543ECAC /dev/disk2
If you want to leave a gap of 100 MiB between your Windows partition and the new volume use the following command instead:
sudo gpt add -b 1563377664 -i 5 -s 390147464 -t 48465300-0000-11AA-AA11-00306543ECAC /dev/disk2
Quit Terminal and open Disk Utility. Erase the newly created partition, format the volume (JHFS+) and rename it.