Capt, only you can decide if the money is wasted or not. I strongly suggest adding the hydrated lime with the alum for 2 reasons here.
First, your kids want to swim and the alum alone will make the water very acidic. Not dangerously acidic, but enough that it will make their eyes burn when the water gets in them.
Second, the only thing that can cause "residual" issues is a pH below 5.4 that will allow the aluminum to dissolve into the water and be absorbed by swimmers/fish...but that is so acidic the kids won't want to swim in the pond!
If you have a lot of open, exposed clay, adding alum may only last till the next rain event.
