Brian,
No man should ever have to justify buying a backhoe!!
However.... I did install my own inground liner pool with a 580 Case. Besides how many buckets full it takes to create the hole it's necessary to have the reach from enough locations to dig & remove spoils. With a big machine there's less locations needed, less moving that must be done immediately, less time involved overall. With a smaller hoe one is at the mercy of time & weather. The goal is to get the hole dug & pool in it ASAP. One good rain can fill the hole back in to the point that it cannot be easily redug, especially with a small machine. Also with a liner pool the hole has to match the liner very closely. Are you experienced enough to do this? Failing the project to where she doesn't get the pool would be a bad move. Do the man thing - buy her a pool - buy you a backhoe. It's a fair deal. MikeD74T