Is it permissible for a widowed mother, who has a pension of 7120 from which her three children receive a share, to take from her children’s money to cover her unmet needs, or for travel, or house renovations, or Hajj? And would this be considered consuming the orphan’s wealth unlawfully?

Allah Almighty has magnified the right of the orphan and forbidden consuming their wealth except in the best way.

Therefore, the guardian of the orphan must fear Allah Almighty regarding the orphans' wealth, not taking anything from it except for spending on them. There is no harm in the guardian spending from their wealth for their benefit, such as renovating the house they live in, and other beneficial interests that accrue to them.

However, regarding the obligation of Hajj, it is not permissible for the orphan's guardian to take from their wealth to perform Hajj. If she is capable of performing Hajj with her own money, then she must hasten to fulfill the obligation. If she is not capable, then Allah has relieved her of this obligation, 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, provision and residence); and whoever disbelieves [i.e. denies Hajj (pilgrimage to Makkah), then he is a disbeliever of Allah], then Allah stands not in need of any of the ‘Alamin (mankind, jinn and all that exists)).