Is it normal to have intrusive thoughts about killing your family?

An occasional thought that flits by, dissipates quickly, likely not an issue. But by definition, "intrusive" means a thought that nags, disrupts, is unwelcome in frequency, intensity. It would be worth finding a therapist to get to the reason, the source—and to find better ways to defuse or address these thoughts. They aren't there "for no reason at all." With a clearer sense of the reason, you can seek better ways to address the root cause.