My British North America TL has a mix of right-handed and left-handed driving. This originates, of course, from the customs of the original settlers (the French and Dutch drove on the right, while the British drove on the left.) Thus each realm (state) has its own road rules:
Canada: right (French heritage)
New England: left (very English)
Pennsylvania: right (Dutch heritage)
Virginia: left (again British)
Florida: right (Spanish influence)
Appalachia: right (wagon teams etc. from Virginia kept right)
Lacustria: right (Canadian and Pennsylvanian influence)
Oregon: left (just like British Columbia OTL)
It is surprising to note that most Americans will still drive on the right after a British victory in the Revolutionary War, and that left-hand driving is isolated to Oregon, New England and Virginia.
Lacustria's annexation of the Lacota Territory proves an interesting case study in this ATL of a change from left-handed driving (primarily stagecoaches to Oregon) to driving on the right.