All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is imperative that a Muslim fulfils all obligations and covenants since Almighty Allah said, "O ye who believe! fulfil (all) obligations"{Al-Ma`ida, 1}, and the Messenger of Allah(PBUH) said, "Muslims will be held to their conditions"{Related by Bukhari}.
In fact, health insurance agreement includes conditions and regulations that determine beneficiaries, namely wife and children. Therefore, it isn`t permissible for non-beneficiaries, although they under the prime insurer`s guardianship, to use the beneficiaries health insurance because that goes against the conditions and regulations of the afore agreement. Moreover, guardianship differs from parenthood and doesn`t take its rulings.
In conclusion, it is permissible for your(Asker) employer to adjust health insurance regulations to cover the children under your guardianship, if that is possible. And Allah knows best.