David,
Sounds like most of your plans are on track except for the 10/2 UF cable. The NEC requires an insulated ground in your wiring method to a pool.
If you decide to run cable (for whatever reason you chose) it needs to be 24" below grade. PVC conduit can be 18". If you mount the post closer than 5' to the pool then a regular outlet is not going to work, a twist-lock outlet must be used to keep anyone from plugging anything in and somehow it ending up in the pool. But if you mount it 10' away, it will be ok with the GFCI outlet. Keep in mind the cord on the pump may not be 10' long, some are, some aren't.
A bond wire (minimum #8awg solid) must be installed from the outer casing of the pump motor to the metal parts of the pool. This is done to make the metal of the pool and the metal of the pump "the same". Limits differences of potential between the two.
The only benefit to driving a ground at the post would be for lightning dissipation. The earth MAY NOT be used as the sole means of ground. So driving one there is not much of a benefit. Actually, the one at the house is for the same purpose, more or less. A fault to ground will always try to go back to the point of origination, using the path of least resistance, of the electric supply. So trying to coax it to go back through the earth, well.........lets say it would take it a day or two. The insulated wire from the house will serve that purpose very well. It will also make the circuit breaker open where as the ground rod won't.
I hope this helps you. And hopefully I haven't confused anyone.
By the way........the lad at Home Depot had a code book he was looking at.......? I can't find anywhere in there where it says only if you go through a garden you have to use conduit. They do try to hire people knowledgable in trades when they can, but they have to take breaks too, and some poor lad will take his place.