What is the priority in distributing the aqiqah among relatives? Should the husband's paternal aunts and his relatives be given precedence over the wife's brothers, especially given the scarcity of what remains to be distributed to her family?

There is no specific Sunnah regarding who should be given the meat of the 'Aqiqah, but it is generally better in matters of gifting to give to relatives, as it involves maintaining kinship ties. The husband is the owner of the 'Aqiqah, and his gifting it to his own relatives is better than gifting it to his wife's relatives. If it is possible to combine giving to both their relatives, that is good.