Is it permissible to give a monthly charity to the poor children of the maternal uncle and his wife, knowing that the maternal uncle is well-off but does not spend on them, claiming that he is paying installments to the bank?

Giving charity has a great reward, and it may be accepted even if placed in the hand of a harlot, a rich person, or a thief, due to the hidden wisdom therein. As for your question, your cousins and their needy mother are more deserving of your charity than others, because giving charity to needy relatives carries a twofold reward: charity and maintaining kinship ties.