Should he do Hajj on behalf of his deceased father who did Hajj, or on behalf of his elderly mother who has not yet done Hajj?

 

ake
her pleased with me”, there is nothing wrong with your asking her to be
pleased with you in this world. But with regard to asking her to be pleased
with you in the Hereafter, this is something that cannot be guaranteed in
this world; it is something that one cannot be certain about. 

The Hereafter is something unknown (ghayb) and no one
can be certain about anything with regard to it. 

So continue striving to please her and honour her until you
attain that. 

With regard to your father, your du‘aa’ for him is better
than doing Hajj on his behalf, so offer a lot of du‘aa’ for him.
“and say: ‘My Lord! Bestow on them Your Mercy as they did
bring me up when I was young’” [al-Isra’ 17:24]. 

And Allah knows best.