I Had a goose long ago before I lived in a place with a real pond.I too did the kiddie pool thing. I think we even dug it into the ground.I remember dumpng it every day.
You can add mosquito dunks they won't harm the ducks but why aren't those spoiled ducks eating the larvae? Ducks are piggish animals I might say I change our ducklings drinking water 3 times a day and cannot wait til they have the whole pond to eat ,swim and poop in.
The fish happily eat the poop sometimes following them around waiting for their next meal to drop !

if you dump all the water out on the ground it kills the mosquito larva. If you do it every week on the same day you should not have a problem with mosquito going all the way from egg to adult. It should take them more than a week to go from egg to adult. here is off the internet.

The egg, larvae and pupae stages depend on temperature and species characteristics as to how long it takes for development. For instance, Culex tarsalis might go through its life cycle in 14 days at 70 F and take only 10 days at 80 F. Also, some species have naturally adapted to go through their entire life cycle in as little as four days or as long as one month.

You can also skim the egg rafts off the surface with a fine net. feeder goldfish will eat those that hatch in clear water that is not replaced such as rain water collectors.

Hopefully you have a garden for that great fertilizer water.