What is the Islamic ruling concerning a wife whose husband does not pray, and she is observant of religious duties? Should she cease her religious commitment because of his aversion and lack of interest, or should she continue her devotion alone, and how can she raise her children religiously in light of this contradiction?

You are not permitted to abandon your religion, cease praying, or neglect other religious duties to please your husband, because obedience to Allah supersedes all other obedience. Continue to gently advise your husband to perform the prayers; if he responds, then all is well and good. If he does not respond, then according to the majority of scholars who do not consider one who abandons prayer out of laziness to have left the fold of Islam, there is no harm in you remaining with him and continuing to advise him. Continue to raise your children well, even if your husband is remiss in that regard.