With Britain distracted militarily by Napoleon, further collaboration with France isn't really necessary- France itself, too, would have been tied up with Napoleon. I think instead just a stronger political and military leadership would have tipped the balance- especially if coupled with a lack of good leadership on the British/Canadian side. I know that American offensive operations in the first half of the war (actually more than half, but the part before Waterloo freed up British troops from Europe and hence the part most likely to have allowed an American victory) were largely bungled by their commanders (although most of my knowledge comes from Canadian histories of the war, and so is perhaps a little biased). There were also several turning points which were quite evenly matched and turned in Britain's favour mostly by flukes. I can name a few if you need help, I'll just need to look them up. I would say, however, that an overwhelming victory is unlikely- forces on both sides were pretty evenly matched. Therefore, an initial American victory would probably be met by a British counteroffensive from remaining North American bases farther north against American coastal cities, plus a reconquest of sorts up the St. Lawrence, after the Napoleonic Wars.
Aha! Perhaps if the American army was stronger by 1812! That might be the turning point you need, especially if it included better military leadership. A further hindrance to American offensives was the fact that they relied on poorly trained and equipped militiamen who vehemently adhered to their one-year tours of duty, often cutting offensives short before they made much headway.
Hope that helps, remember, I've got lots of Canadian propaganda here if you need more 'information'.
-John
