Dr. Muzammil H. Siddiqi, president of the Fiqh Council of North America, states: when parents reach a certain old age, it is better that children make Hajjbadal, that is, Hajj on their behalf. As they may not be in a good condition to go to Hajj. In sha’ Allah, they will receive the reward and the one who goes in their place will also receive the reward for doing this good deed on their behalf.
For Hajj badal the rule is that only that person should do it who has done his or her own Hajj first. So if the children have already performed their own Hajj, they can make the Hajj on behalf of their parents. Otherwise, they to first do their own Hajj, and then later, if they can, do the Hajj on their behalf. May Allah bless us.