Since your wife is negative for HBsAg and that your kids were vaccinated, it is unlikely that they are infected.
Mutations mean change in the genetic material which may have an impact on treatment.
Not all who are positive for HBsAg develop cirrhosis and cancer.
If you have still not developed cirrhosis, check your HBV DNA levels and decide on antiviral treatment.
Complete eradication of HBV cannot be guaranteed with any medicine.