I let my players change things, if it's logical that it would follow from their actions. I always start out adhering closely to the history as written, but if the PCs do something wild, I go with it.
In my current game, due to the PCs actions in the Quasi-War with France, the US Navy is taking far more forceful actions in the First Barbary War than actually happened. One of the PCs has a hat-on for the Brits as they stopped his half-fitted-out brig on its way from Philadelphia to Washington and snatched three seamen. He is, I think, determined to force a war between the US and Britain before 1812, and is well on his way to getting that done. Some of his actions:
He caught a British spy and killed another one in a fight in Philadelphia.
He has nearly convinced the Administration that the Brits are behind the Barbary depredations on Americans. He may, in fact, be right.
He refused to salute the British admiral of a squadron near Gibraltar.
When they took a small Algerian port to use as a base - he doesn't trust Port Mahon or Gibraltar - they installed a puppet Bashar to rule it. The British orchestrated and funded a coup d'etat and the new Bashar threw the Americans out. The group, under his leadership, took it back by organizing and supplying a popular revolt at night, during which the PC's ships blew up the fort, entered the harbor, and destroyed a careened British frigate with mortar vessels borrowed from the Spanish. They intend to claim they thought it was an Algerine vessel, but they knew it was British. The mob didn't help things by killing the British consul and looting his home.
I have no idea how far they are going to take this. The PCs are fabulously famous right now - like Decatur was in real life - and public opinion seems to be behind them. It's only a generation after the War of Independence, after all. They've already changed history, and seem determined to change it again.
-mice