Is it permissible to resort to a Riba-based bank to purchase a house in order to avoid losing a down payment?

Firstly: If what took place was merely a promise to purchase, then the seller is not entitled to take the down payment (10% advance) if you withdraw; because the down payment is due with the contract, not with a mere promise. If the contract is not finalized, you are entitled to get your advance back. The most the seller can take is the actual damage incurred due to the breach of promise.

Secondly: If the contract has been finalized, your brother's withdrawal requires the sale of his share, and you are not obligated to buy his share. He must search for a buyer, otherwise he remains a partner until everyone agrees to sell to an external party.

Thirdly: The solution is to look for a buyer for your brother's share or a partner to replace him. It is possible to agree on selling his share after a period at an estimated price at the time of sale (diminishing partnership). Usurious loans must be avoided regardless of potential losses, as they are forbidden in Islamic law.