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I am afraid that if your Wife's brothers do indeed wish to receive their due one third share, Stamp Duty will be payable by your Wife on the two thirds share, as this sum is classed as chargeable consideration for Stamp Duty purposes.
(As you are aware, no Stamp Duty is payable on the one third that your Wife is entitled to).
The only way, therefore, that Stamp Duty would not become payable is if her brothers were happy to give up their one third inheritance each, and agreed to give the whole house to your Wife. In such circumstances a Deed of Variation of her Father's Estate would need to be drawn up, stating that her 2 brothers were prepared to forego their one third of the property and that it should instead pass to your Wife. I doubt very much that your WIfe's brothers would agree to this and forego part of their inheritance. Even if they did, you are looking at legal fees of approx £500 plys VAT in drawing up the Deed.
So, I'm afraid your Wife is really stuck with the Stamp Duty issue.
As rgeards the "additional costs" to be incurred by the Solicitor in dealing with a "purchase", these don't have to be that expensive. It would be normal for searches to be done for a Purchaser, but if your Wife did not want these doing, she can instruct her Solicitor accordingly. Likewise, as it is a family arrangement, the Solicitor can dispense with a Sale Contract and merely prepare the Land Registry Transfer document, which is then signed by your Wife, as Executor, and Buyer.
I am sorry this is not the answer you were looking for, but it sets out the legal position.