You will need to have a blood test for “HBs antibodies” to tell whether the vaccine worked well enough to provide good protection from the virus. That is the name of the type of antibodies the vaccine produces. Your doctor can easily arrange for the test to be done and help you interpret the result.
About 95% of people make enough antibodies to protect them from HBV, so odds are very good you and your children are safe once the vaccination series is completed. Once that happens, the risk of getting the virus is extremely low. Also, transmission from your wife will not occur from casual household contact. There is a risk of sexual transmission, or through contact with her blood, but that risk gets lower as her HBV DNA levels get lower due to tenofovir treatment, and transmission will be blocked by the vaccine if enough HBs antibodies are made.
I am sorry your family is having this stress, but it seems like your wife is receiving good care and your family is doing the right thing to protected yourselves.
I wish you the best,