How can family members who do not pray be helped and encouraged to do so, while fearing a weakening of one's personal commitment?

Abandoning prayer is one of the greatest sins; indeed, it is considered disbelief by some scholars. Therefore, you must strive to advise your family in a way that does not alienate them, using appropriate da'wah (invitational) methods such as lectures and pamphlets. You should also adhere firmly to righteousness and seek out committed friends who will help you in obedience to Allah.