This is one of those classic "but it works" death traps that the untrained handyman types come up with. The short version:
There is NO substitute for good design, especially near water!
I run into this sort of thing all the time ... guy wants to cheap out, run as little wire as possible ... 'all I need is 220' they swear. Then. before the sod takes root, they wnat to 'make' 120 for 'just alight,' etc.
NO. NO. And again- NO. What part of 'NO'can they not understand?
Your 'service' is where your meter is. Period. Let the PoCo bring in just three wires.
YOU, on the other hand, get to run FOUR wires. A sub is a sub is a sub. Period. Plus, since you're adding a panel, you ALSO get to bang in a ground rod.
Which brings us to issue #2: Just what size panel? I can't say I've ever seen a 20 amp panel before. 20 amps is all you'll get, over any distance, with #10. Maybe even less.
Chances are, that UF isn't buried 2ft down either. So - do it right, or pass it by. Dig deep, run big pipe, and four wires. Expensive? Well, you get what you pay for. Had the guy designed well in the beginning, he would not be crying today.
