Is it permissible for my husband to send the household allowance to his mother for her to give to me, knowing that I have a bank card to which he can transfer it directly?

It is permissible for the husband to pay the maintenance to his wife himself or to appoint someone to deliver it to her, as indicated by the hadith of Fatimah bint Qais. If the husband's mother orders that the maintenance be paid through her, then obedience to her is not obligatory, because there is no sound benefit for her in that. The husband can send a part of the maintenance through his mother and send the other part directly to the wife.