I frequently lose temper and misbehave (which I shouldn’t) because my family prefers customs of our forefathers over Islam. They remain in search of my mistakes to show me that I am in fact a hypocrite following the portion of deen which suits me. If I start living away from them for the sake of Islam, is it legitimate? Does kinship also implies that we should live together or in same city?

You must try your level best to control your temper and respect your
family. However, you should explain to them in a respectful manner,
that they must stop praticing these customs that go against Islam, for
their own good towards Allah.
Your behavior represents your level of your Iman! It is not an excuse
that you lose your temper as this is a sign of ignorance and lack of
sincerity. Try your level best to stop these whispers of satan and
learn how to control your anger and be diplomatic for the sake of

Please visit here for detailed fatwa information directly from highly respected scholar