What is the Shariah ruling concerning the money the father received from his work at UNRWA, given that it includes profits from funds that were forcibly deducted and invested in illicit activities, and must the amount that his children deem usurious be extracted?

If the deducted amount was invested in something displeasing to Allah, then it is not permissible to claim ownership of the unlawful profits. Only the principal capital may be owned, as Allah Almighty says: (But if you repent, you may have your principal – neither do you wrong, nor are you wronged). As for the profits, they should be spent on Muslim welfare, such as building hospitals and orphanages, and not left to the investment entity.