Precipitate usually means "bringing something on" or "making it happen" — and not always in a good way. An unpopular verdict might "precipitate violence"
Jackson then sent a peremptory order, not only to forward provisions, but to join him at once with his troops.
Peremptory is used to describe commands, statements or orders of the kind that people obey because they are given with an air of authority — they are often barked. Think of doctors in operating rooms, growling peremptory commands at nurses, "Scalpel," "Forceps," "Chewing gum," and you'll get the idea.