I would get the tooth bar for the loader and skip the backhoe. Depending on how hard your soil is maybe also get a boxblade with rippers. You could then set the ripper 4-6" deep and drive over where you are digging which would loosen it up before using the loader. You could even use the boxblade to pull the loose dirt into piles before using the loader to move, load, or what ever you are doing with the dirt.
The loader on these tractors are pretty powerful and can dig pretty well. For example I have used the loader on our kubota
M7040 to dig a lot of 12-18" deep trenches and have also dug two large 5' deep, 7' wide, 15' long holes and it doesn't have a tooth bar.
Seeing what you just posted, I would definitely get the boxblade. This would let you pull the dirt away from the pool and could be used to maintain the driveway.
Ed