Corals are VERY old evolutionarily speaking. they lack claws, they cannot run away, and their stinging parts do not harm the animals that might eat them - only the animals they want to eat and each other... so how do they protect themselves from predators?
TOXINS!!!
These toxins make corals a valuable source for medicines, actually.
And the bit about allergies is very serious - every encounter after an allergic reaction is established increases the immune response - the reaction itself may do more damage than the allergen! But this is different than suffering from the toxin.
The toxin can hurt/kill you if it gets into your blood stream through its own cascade reaction. Allergies are different, though.
Those who are allergic, on the other hand, need only to contact not just the toxin, but other parts of the coral as well. Any part of the coral that gives off a protein can trigger an allergic reaction (a different cascade reaction than the toxin causes), and there are receptors for these allergens ON OUR SKIN!!!!! So you can't rely on "i have no cuts on my hands/arms" if you are an allergic person.
Without knowledge of specifics, this is the way these two things differ - hope that helps...
But i have to wonder how your kids can get their hands in the tank... Maybe my kids are just super-cautious (come to think of it, they pretty much are...) but there are lots of other dangerous things in our homes - like our OVENS! if we take the proper precautions, we can keep our families and our tanks safe, I hope!