There's no way anyone can offer you good advice on this, without seeing the pool walls. Keep in mind that acid-washing works by corroding off the top layer of plaster, leaving it whiter, but also rougher and more susceptible to stains.
The dead rat is an aesthetic issue, but not a sanitary one. Once you clean up and chlorinate, there's no problem. (Keep in mind, that if you drink treated river water like most people in the US do, there've been much worse things then dead rats in that water!)
If you are going to drain, and you are on a hill or hillside, there's no problem. But if you are in a flat area with wet ground . . . it's another matter. Better think twice, in that case. If you're determined to go ahead, did a post hole 4' deep next to the pool, and let it stand. If it stays dry, you should be OK. If not, don't drain, no matter what your wife says.
I can promise you she REALLY won't like the concrete boat you'll have sitting up out of the ground all cattywampus.
Ben
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