Sometimes you just deal with the behavior--I think kids get in to bad habits.  I would probably prepare myself for about 3 weeks of correcting the picking a fight behavior every time it happened. 

  I would start by having a family meeting about courtesy, maybe even etiquette--pleases and thank yous and napkins in our lap and introducing yourself and respecting people's ownership of their possessions and thank you notes and the whole nine yards.  NOT about fighting, about courtesy.  Let them know you expect them to be courteous to each other.  Have a nice dinner where you can practice table manners.  Help the little boy with thank you notes (the big sisters can do the actual writing) after his Birthday.