The invasion would have come from main land USA.
Rommel-out
Not likely -- the logistics or launching an invasion without a close forward base against a force as strong as the Wehrmacht with forces as inexperienced as they would be without the blooding of "sideshow" theatres like Tunisia and Sicily would have been a crippling obstacle.
Also, the Luftwaffe would probably have been intact and I doubt that with WW2 technology a sustained strategic air campaign against Germany would have been possible across the Atlantic ... and it was fighting the P-51's that finally broke the Luftwaffe (and fuel shortages).
Only way to get fighter cover would've been to park a hundred fleet carriers in the eastern Atlantic.
I think, given enough time, US might have had the industrial capacity to do that (although only without fighting Japan at the same time), but would they have bothered? -- if Hitler was crazy enough to pre-empt and say bomb New York etc... then maybe, but then war would've dragged into late 40's (ok, all depends what would have happened on the Eastern Front -- Soviets broke the German army's backbone, the USAAF the Luftwaffe)
I guess nukes would've been the only option ... and would've been used even over Europe ... at the time they were only considered by most military leaders (who actually knew about them) as just a "bigger bomb."
As to Commonwealth keeping up the war -- not sure about that.
India would've surely taken the gap and declared independence -- and no other Commonwealth country at the time had the industrial or population base to carry on more than a harassment/guerilla campaign.