Praise be to Allah.
It is permissible for a Muslim woman to accept support and gifts from her non-Muslim father, so long as that will not result in her giving up anything of her religious commitment. The Prophet (blessings and peace of Allah be upon him) accepted gifts from al-Muqawqas and the Negus (an-Najaashi), who were both Christians.
Commercial insurance of all types is haraam, including health insurance, because it is based on ambiguity and gambling. But if a person is compelled to do that, there is no blame on him and the sin is on the one who compelled him. See the answer to question no. 133341
If your father has taken out this insurance, then he has taken care of that for you. If he refuses to pay the insurance, it is permissible for you to take out insurance for yourself, because you are compelled to do that. But we do not think that you should take it out unless your father actually refuses to do that.
We ask Allah, may He be exalted, to bless you and help you and guide your father and relatives.
And Allah knows best.