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Lord Liverpool offered Wellington command of the British Forces in North America late on in the war and Wellington declined largely beacuse he felt he would be expected to produce a total victory and he regarded that as impossible (probably correctly)and that the priority should be the defence of Canada after a few other refusals the job went to Wellington's brother in Law Pakenham with disastrous consequences for Britain.
Suppose Wellington had accepted? If he had gone early enough he would probably have prevented the burning of Washington. Wellington was noted for treating civilians in areas he had conquered with respect as in India although Ross may well have taken a softer approach but for partisans. However the offer appears to have come later. He would however almost certainly have avoided the debacle at New Orleans leaving Britain in a stronger position albeit after the treaty was signed and with a better reputation (and removing the source of a well known folksong). However would it have had an adverse effect on Europe and could ha have been back in time to tackle Napoleon at Waterloo.