Is it permissible to agree with a partner to deduct usurious profits from the capital, and to pay the remaining amount in installments as a long-term loan, taking into account currency fluctuations and the fact that the money belongs to others?

Your agreement to deduct the profit portion from the principal amount and pay the remainder in installments is correct, because the mudarib (investing partner) is liable for the capital that was not used in trade. As for the funds belonging to the questioner's mother and siblings, he is not liable for them since he acted as an agent; however, there is no harm in him voluntarily returning their full principal amount.