Is it permissible to go for Umrah with a Mahram who does not pray or fast and holds incorrect beliefs about the religion?

It is permissible for you and your mother to travel for Hajj with your corrupt maternal uncle. Some scholars hold that a disbeliever is considered a mahram (definition) for a woman whom he is forbidden to marry permanently, so a corrupt Muslim would be even more so. Continue to advise your uncle to abandon neglecting prayer, for whoever abandons it out of denial and rejection of its obligation is a disbeliever by the consensus of scholars, and similarly for denying the obligation of fasting. Some scholars are of the opinion that abandoning prayer out of negligence and laziness is an act of disbelief, so he must repent and make up for the missed obligatory duties.