Is the money saved for Hajj, from which some was spent on young children, considered my property or the children's property? And to what extent is it permissible for me to dispose of this money?

If the state provides financial support to the father of the children, then this money is his property, and he must perform Hajj if he possesses the means for it and it exceeds the expenses of his dependents.

However, if the state provides financial support directly to the children, the father is not permitted to take from their money to perform Hajj, because a father may not take from his child's money unless he is in need. This is the view of the majority of scholars.

The Hanbalis, however, hold the view that a father may take from his child's money whatever he wishes, whether he is in need or not, provided it does not harm the child.

The preferred view is that of the majority of scholars.