I am studying in a western country at the expense of my home country and my family lives with me. The country where I study offers financial aid to us because we have children. Is it permissible for me and my wife to perform Hajj with this money noting that I fulfill all the needs of my family because the financial grant secures an acceptable standard of living.

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If the country which donates this grant stipulates that it should be spent on the necessities of the lives of the children such as food, drink, and clothes, or considers this grant the private property of the children, then it is impermissible to spend it otherwise. This is based on the statement of the Prophet, sallallaahu ‘alayhi wa sallam, "Muslims should abide by their conditions in what is lawful." [At-Tabaraani] 

However, if the donating country does not stipulate such a condition, meaning that the money is donated only because your family includes children, then you can spend it on whatever you like of lawful things or that which are done to draw close to Allaah The Almighty, like Hajj and the like of it. But, doing this must not result in falling short in fulfilling the rights of the children. Please also note that it is not a condition of the validity of Hajj, be it obligatory or voluntarily, that it should be performed from the pilgrim’s money, although spending on Hajj from one's own money is better and earns a greater reward from Allaah The Almighty. We ask Allaah The Almighty to Accept our good deeds and yours.