Is the intermediary considered to have betrayed the trust if he delivered it to the intended person who, in turn, lost it?

You are acting as an agent for your mother and sister in entrusting the money to the Mudarib (investment partner). An agent is a trustee and is not liable unless there is transgression or negligence. You did not deceive them; rather, you were diligent and informed them of what you knew, and you invested your own money alongside theirs. The man is the transgressor, and the sin of his transgression is upon him, and he is liable for the money. If he does not return it, then everyone who has a right will receive their due on the Day of Resurrection, as Allah Almighty says: "And We place the scales of justice for the Day of Resurrection, so no soul will be wronged at all. And if there is [even] the weight of a mustard seed, We will bring it forth. And sufficient are We as calculators." (Quran 21:47) And the Prophet, peace and blessings be upon him, said: "Whoever has wronged his brother concerning his honor or anything else, let him seek forgiveness from him today before there is no Dinar or Dirham. If he has good deeds, they will be taken from him commensurate with his wrongdoing. And if he has no good deeds, then some of the evil deeds of his companion will be taken and laid upon him."