What kind of powers did Hera's children have?

Answer 1

Hera's children had diverse "powers". She being the goddess of family and marriage, she wouldn't have bastard children, and her only children are, therefore, also children of Zeus, thus being Gods. Hera's children were: Ares, Enyo, Hebe, Eilethya, Hephaestus, and Eris. Ares was the God of War, Hephaestus, was, according to Wikipedia, the god of blacksmiths, Metallurgy, fire, volcanoes, technology, among others. Eris was the goddess of discord. As you can see by these examples, Hera's children all had different specialities and different powers, and therefore, we cannot say Hera's children had a certain "kind of power".

Either way, if you are asking about the Percy-Jackson-demigod-kind-of-power, Hera didn't have demigod children because of the reasons listed above.