Will the father be held accountable for not giving the sponsor what he promised him of profits after his trade became large, and are the losses the family is experiencing due to this money, and does the mother bear the sin of her silence concerning that?

If the agreement is a corrupt Mudarabah (definition) (a loan with interest), then the guarantor is entitled to his capital along with the profits, and your father is entitled to a similar wage. If the agreement is a guarantee and not a Mudarabah, then the guarantor is not entitled to anything in return for his guarantee.

Furthermore, your father's squandering of his money and his neglect of his family is a great sin. And the mother is sinful by her silence regarding the father's refusal to pay the guarantor's due, if she is aware of it.