Same thing happened to me, except, no kids I could blame.. ;)
Your setup sounds like mine, in that the valve is right up against the tank then a 90 bend to the side of the trailer. The valve handle has a really long extension to the valve.
But, I don't have a sealed under carriage, so it was easy to get to.
What I did was leave the valve open all winter. I left the cap off the end as well... This allowed the tank to dry out completely.
Come Spring and I got the motivation to do the job, I removed the valve assembly and cleared the little tiny piece of TP that was causing my leakage.
I think it would take several gallons of water to fill up the pipe and then I don't think the way the TP was wedged into the groove so tightly, that it would have simply 'dissolved' to where it wouldn't be there anymore even if it soaked for a year...
I tried to back flush, shove the hose up the pipe, use the spray wand and nothing worked. Until I took the valve off..
Good luck with whatever you do!
Mitch