Is it permissible to help needy relatives who do not pray, knowing that there are other poor people who are committed [to their religious obligations]?

Your act of helping your relatives is valid. Allah praised the Companions for feeding prisoners, and permissible is kindness to non-combatant disbelievers. Charity was accepted for the adulteress, the rich, and the thief, because it might lead the adulteress to chastity, the rich to spend, and the thief to desist from stealing. Do not regret helping them. However, if you cannot extend help to all, then giving to the pious is more fitting. You must also invite them to prayer and explain the danger of abandoning it. If cutting off aid prompts them to pray, then you must do so.