Welcome to AC...
Let me first recommend that you get yourself a good test kit for your tanks. Make sure you have tests for ammonia, nitrItes and pH. You'll likely at one point or another want a nitrAte kit...but that can wait for now.
Without having a ton of details on the tank specs and water parameters, you're definitely experiencing what is known as cycling. Read up on the Nitrogen cycle.
http://www.skepticalaquarist.com/nutrient.html
To summarize, your fish produce ammonia as a waste product. Ammonia is toxic to your fish and will begin to build up in your tank as soon as you add fish. There is a beneficial bacteria that will begin to build in your tank that will process the ammonia into nitrItes (this build up takes some time so your fish are exposed to ammonia during this time). The nitrItes are also very toxic to your fish. Fortunately, there is a second variation of beneficial bacteria that builds up and processes these nitrItes into nitrAtes (once again, while we wait for the colony to grow, your fish are bathing in toxins). In controllable concentrations, nitrAtes are harmless to fish. When the bacterial colonies build up enough to fully process the ammonia and nitrItes as quickly as they are produced, you have what is known as a fully cycled tank. At this point we do weekly/bi-weekly water changes to keep the level of nitrAtes at a reasonable level. This whole cycling process can take anywhere from 4-8 weeks.
I would say right now you're experiencing a spike in the levels of ammonia and that is why you've lost your fish. Since I suspect you won't be able to talk your daughters into staring at an empty fish tank while you "fishless" cycle your tank, you'll be best off picking up 2-3 danios for each tank. They'll survive the cycling process pretty well.
Things you should do to help your cycling:
1. Immediately do a 50% water change on both tanks with clean (dechlorinated) water to decrease the toxin levels.
1a. If you have access to a fully cycled tank (friend, relative, etc.) ask them for a bit of their filter media. This is where the majority of your bacteria will colonize and adding this to your filters will help the cycling process along.
2. Keep a close eye on your ammonia and nitrite levels and keep them low by doing 30-40% water changes with clean (dechlorinated) water.
3. Don't add any more fish until your cycling is complete...once again, this will be when your tests show 0 ammonia and 0 nitrItes for several days in a row.
4. Read through as much info here and elsewhere as you can on cycling a tank.
5. Don't believe all the hype about chemicals that help the cycling process. There has yet to be a tried and true chemical way to get cycling done any faster than the natural way.
I hope that wasn't too much for one post...please ask any questions you might have, I'll be glad to clarify...this is where the single most important part of fishkeeping will start to rear its ugly head. You must have patience young Skywalker. The cycling process can be frustrating and will seem like it's going to never end...but we've all been through it and will help you out.
Good Luck