Is it obligatory to slaughter the Hady (sacrificial animal) on behalf of a father who died after performing Hajj as a mufrid (performing Hajj only) without having slaughtered it, and what should his family and mother, who performed Hajj with him, do?

There is nothing (no sin) upon your father—may Allah have mercy on him—if he performed Hajj mufrid (singly), as the hady (sacrificial animal) is obligatory only upon the qarin (one performing qiran (definition) Hajj) and the mutamatti‘ (one performing tamattu‘ Hajj), based on the Almighty’s saying: "But whoever performs Umrah (definition) [in the months of Hajj] then [continues on] to Hajj, let him offer what can be easily obtained of sacrifice." However, if the hady became obligatory upon him due to abandoning an obligatory rite of Hajj (such as throwing the pebbles, or staying overnight in Muzdalifah, or entering ihram (definition) from the miqat (definition), or staying overnight in Mina), then the hady must be offered from his estate.