Is it necessary to go to the mosque to say prayers, or is it acceptable to say prayers at home?

I want to ask that whether going for prayers to the mosque is necessary, or I can say my namaz at home also. I used to go to the mosque in the Fajr time and say my namaz with jamat. Because we live in a place where there is only three houses who are Muslims and the mosque is also a little far away from our house, though there has been no disturbance or fright of anyone or anything. But my mother tells me to say my Fajr (Morning Prayer) at home and does not allow me to go alone to the mosque at such an early time, as it is still little dark. So can I say my prayers at home? As much as I know saying prayer with jamat is wajib and obeying parents is Fardh. So the status of Fardh is more than Wajib so one has to follow Fardh first, thinking this way I say my prayers at home. Am I correct in my thought? Will my prayers be accepted? What shall I do? As on one side I have to say prayer in jamat and the other side I have to obey my parents. Please help me.