I have some experience of this type situation and disagree with some of the posters.
It is my opinion that if the situation is that the house was left to the three of ye then the brother is perfectly within his rights to cash in his share.
All he was left was a right of residency. That cannot realistically be sold.
If the other two object he will need to get a court order directing that the property be sold.
After all legally he is a one third owner and the Courts will uphold his property rights.
The Court will order that it be sold unless ye come up with a solution.
He cannot sell what he does not own. He does not own a free title to the house, not even one third of a free title to the house. I cannot see why the courts would even consider ordering a sale.
Your father was badly advised to insert the right of residency in the will and then leave it to the three of you. He has not done any favours. This will is typical of many bad wills made in this country and the only people to gain will be the legal profession.
Why, the father has ensured that his children have a place to live. If they got the cash, maybe the money would end up with the bookies or the publican, or invested in some dodgy investment. We have no idea why the father wished to use his property to ensure his children had someplace to live, but he did and why are people trying to second guess that.