To be honest, this is a problem for your mother and brother to hammer out. I'd advise not getting involved.
Certainly, both sides are likely to want to talk to you about it, and for you to take their side, but it's not really your place.
I'm guessing there's a whole LOAD of back story here, as to why your mother and brother don't speak (that's so sad, something horrible must have happened). And really, only they know what went down there, and how it has affected them.
It is not your job, or responsibility, to police either of their behaviours. Remember that.
You also need to remember that YOU have lost a relative you (presumably?) cared about. What do YOU need to happen for this funeral to go off in a way that is as stress-free as possible for YOU?
Do you have a confident, close friend who could keep an eye of the whole mum/brother thing on the day, so you don't have to? You honestly can't stop brother attending (and it sounds like you don't want to), but with help from a friend, you can ensure that if a blow-up does happen, you're not near by, or involved. If the friend is a confident sort, could they take brother under their wing for the duration? "Ah David! I've heard so much about you! Come and tell me everything I need to know, in this cozy corner over here!"
Could you even suggest that mum/brother bring their own trustworthy, most sensible friend, with the sole purpose of keeping them away from each other?
Everyone is on extremely heightened emotions during a funeral. It is not the time, or place for extended discussions on who did what to who.
If mum and brother come face to face, for the sake of getting through the day, could they manage to handle a "oh, how nice to see you! I'm just going to grab a cup of tea." If not for your sanity, then for their own. If not for their own, for the sake of the deceased. The last thing she'd want would be everyone to remember her funeral as "the one where Jean and David threw an absolute fit at each other!"
I'm sorry for your loss. I hope the event goes smoothly in the end.