Is eating by the household members from the food brought by the orphaned children of the sister considered consuming the orphan's property, and how can one act in such a situation without hurting the children's feelings?

A mother has no guardianship over her orphaned children's wealth unless there is no guardian appointed by the deceased father, and the court has not appointed a guardian for them. In such a case, the mother may manage their wealth for preservation only, and she is not permitted to dispose of it except in a way that is most beneficial to them.

Therefore, she is not allowed to give gifts or charity from the orphans' wealth, and you are not permitted to accept gifts from this wealth.

As for mingling with orphans in food and drink, there is no harm in it, as Allah Almighty says: "And they ask you concerning orphans. Say, 'Improvement for them is best.' And if you mix with them, they are your brothers. And Allah knows the corruptor from the reformer. And had Allah willed, He could have put you in difficulty. Indeed, Allah is Exalted in Might and Wise."