I thought it was much simpler than that; if the Will leaves the house to three siblings equally, then they can force the 'stay at home' out.
However this will not be the case if:
1) the 'stay at home' sibling is also named as one of proprietors on the Land Registry title - in which case (in the absence of any other deed of gift) the mother only owns 50% of the equity in the house in the first place, or
2) there is a clause in the Will stating the 'stay at home' can stay there until he wishes to move out. Such a clause needs to be professionally drafted, to avoid the potential for hassle and debate that may otherwise happen.