Is it permissible for an employee to dispose of a sum of money entrusted to him, and is his dealing with a third party permissible, knowing that his employment contract prohibits this, and he only dealt with them due to an urgent need of a relative?

There are two scenarios for settling the debts of another person:

The first is permissible if it involves selling a commodity in installments, which the debtor then sells for an immediate price to settle their debt (Tawarruq).

The second is forbidden if it involves lending money with an increase, or paying money on their behalf for them to return it with an increase, or selling a commodity to the debtor which then returns to the seller or an accomplice. All of these are usury (riba).

If the transaction is permissible, there is no objection to taking a commission fee. If his work is limited to contacting someone who will settle the debt due to no other means of assisting his relative, then there is no objection for him.