Is it permissible for a person to perform Hajj with money from his son while he has outstanding debts to his other children, his son's wife, and his brother, despite owning properties from which he could pay off his debts?

If someone finds money to pay off debts and is able to perform Hajj with it, then Hajj becomes obligatory for them. However, if they have no money left after paying off debts, then Hajj is not obligatory for them, as Allah Almighty says: "And Hajj (pilgrimage to Makkah) to the House (Ka'bah) is a duty that mankind owes to Allah, those who can afford the expenses (for one's conveyance and provision for himself and his family during Hajj)." (Aal-Imran: 97)

And whoever is not obligated to perform Hajj due to their inability to afford its costs, is not required to perform Hajj if someone else offers to pay for it, even if that person is their son, according to the Hanbalis and one opinion among the Malikis.

However, Imam Shafi'i and another opinion among the Malikis hold that Hajj becomes obligatory if the son provides the money, based on the Prophet's (peace be upon him) saying: "Indeed, the best of what a man eats is from his own earnings, and his child is from his earnings."

This difference of opinion is only regarding the obligation of Hajj, but there is no disagreement regarding the permissibility of performing Hajj. So, your Hajj is permissible, and there is no blame upon you for it.