Stay. A solicitor cannot make court orders - it is not legal. Only a court can do that.
But he should be careful because it is likely that his wife will do what she can to get him out - likely occupation and non-molestation order.
There is a LOT he can do but he needs to be careful:
1.) Record all conversations. He does NOT have to tell her this. Make sure he is polite, courteous and reasonable at all times. Do not hit back if she attacks him and if she attempts to cause an argument walk away.
2.) Keep all interaction with her to a bare minimum.
3.) Keep a diary of all events. Make sure she doesn't find it.
4.) Stop sleeping with her if he is still doing so. Even if she offers - because if she alleges rape or somesuch it is game over'. 5.) Sleep in another room. Put a lock on the door if needed. 6.) Stay until an established routine of good meaningful contact with the children is established. NOT before. 7.) If he is arrested by the police advice him NOT to accept a caution just so you can leave the station' - this is an admission of guilt and it will be used against him.
8.) If there is a divorce looming, seek mediation.
If he leaves he it will be deemed that he has `abandoned the family home voluntarily'.
He is on a well worn path and it sounds like his ex knows exactly what she wants and how to get it. If he isn't careful he will be homeless, with contact for his children dictated by his wife and a caution used against him in court if he tries to do so.
I would strongly advise he join Families Need Fathers NOW. Do not delay - your brother's wife has likely planned this a long, long time ago and your brother is likely paralysed by fear and shock particularly as he is ill. Join them NOW - do not hesitate!
If you need some advice, please get in touch with my via PM.
I have seen too many people go down this route and while it is going to be hard whatever he does there is a lot he can do to mitigate the likely damage. Sorry if I am being a bit strident here - most people say `I'll leave it a bit because I have to go to the cinema tonight' or something...! 