The inquirer says: My wife works and she has her own independent income. Her father is elderly and financially incapable of performing Hajj or ‘Umrah, and his sons cannot help him.
My wife – I agree with her – wants to allocate a sufficient amount of her money for her father so that he could perform Hajj and ‘Umrah. My wife and I have performed Hajj (praise belongs to God). Is it permissible for my wife’s father to make Hajj or ‘Umrah?

There is no objection to the wife’s father performing Hajj or ‘Umrah, where she pays the expenses from her personal wealth. This is an act of piety, kindness and maintaining family relations; once the donator donates his money for Hajj, the money becomes the property of the recipient, and the ability to perform Hajj – which is required – is achieved, and it achieves what Allah said:
Whoever enters it is safe. Pilgrimage to the House is a duty owed to God by people who are able to undertake it. Those who reject this [should know that] God has no need of anyone. [3:97]

The answer to the question is know from the above.

Allah Sublime and Most High knows best.