Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There are laws and regulations governing government health insurance and it is imperative upon insured persons to abide by them since Islamic Law commands a Muslim to honor the contract and fulfill its conditions. Thus, it is unlawful for a Muslim to resort to lies and tricks to get money from any entity particularly a public one because transgression against such entity is a transgression against the rights of all citizens. In this regard, Allah The Almighty Says {What means}: "O ye who believe! Eat not up your property among yourselves in vanities: But let there be amongst you Traffic and trade by mutual good-will: Nor kill (or destroy) yourselves: for verily God hath been to you Most Merciful!" {An-Nisa`, 29}.
In conclusion, if your delivery was really an emergency and the government insurance covered a portion of the costs based on that, then you are cleared from liability before Allah. But, if it wasn`t an emergency and you could have delivered in the nearest public hospital, then the money you have taken from the government insurance directorate is unlawful and you have to give it back in the manner you see fit. However, if you feared that you may be called to account for what you did, then you may donate that amount to one of the public hospitals. And Allah The Almighty Knows Best.