There were quite a few secessionist movements in the Trans-Appalachian region in the early years of the Republic. I'm sure there are plenty of PODs which might have some of them be successful. Jefferson even expected that some of the western territories might eventually break off and wasn't especially bothered by the idea.
Alternatively, if the British end 1781 on a slightly firmer footing (perhaps the French aren't successful in pinning Cornwallis in at Yorktown and his troops are able to escape to New York City), then the British might want peace but are in a stronger negotiating position. The western border is therefore set on the Appalachians rather than the Mississippi. American settlers would still be headed west, though, no matter what.