You still have to go through the legal process of a legal eviction. whatever state you live in you need to know the process. it can be a pain and can take anywhere to 30-90 days. good luck as I hate it that it is a family member you have to evict. hopefully you can do it in a way that doesn't cause bad blood with the family but I can also understand the worry about an estate going to "shambles" as it was put. I just hope all works out for the best as a house is just a shell to live in, family is priceless.
As executor he has all the rights as a landlord and also must go through the same remedies to evict a tenant. it can be a lengthy process. good luck!
Is the house in such disrepair that it is harmful to others? Would the health and home workers say it was unsafe? Has your brother spoken to the nephew about the house, and does he know his father left the home to a brother? If he is hurt by this decision, you may want to do everything legally. Most states require thirty days to notify the occupant of eviction, again unless the house is a wreck. Where will your nephew go. Does he have funds to move? Does he have a family? Trying to put someone out immediately is a very strong action without knowledge as to how the tenant will live. I hope all works out peacefully. Perhaps your brother will be willing to assist your nephew with his move by helping with expensive. This is hard to say when there is little information. Best wishes to you all and I really do hope things work out for the best of all involved.