So I got a question: why would UK ally with Germany to fight the US anyway? That just sounds like such a silly scenario.
Only way I could fathom such an alliance would be a collapse of British government by way of fascist coup'd'tat. This is a lot of fanciful ifs mind you:
--Germany changes timing of Barbarossa
[See below]
--Hitler does not order the Luftwaffe to stop pressuring the RAF airfields in order to target london
--Hitler's V3 comes online and isn't bombed out of existence by RAF
--England is pummeled enough for public opinion to favor a change in status quo
Then maybe just maybe, given the chaos that can occur at such times, Britain might have fallen to Hitler-friendly elements. Unfortunately, I can't see that doing anything but fragmenting the English and dropping the country into a nasty civil war (why would a Brit suddenly be amenable to a government friendly to the guy who'd blitzed them for the past few years?). Assuming the people are somehow cowed and
don't engage in a civil war, and the RN doesn't defect and the commonwealth doesn't implode.............
Then it's a
real problem for the Allies. Against the RN and without England to launch from, an invasion of Europe proper becomes as impossible for the USA as it is for Germany. Actually, with Canada as a launching point, it becomes
easier for germany to invade the USA. Lets assume Hitler wasn't that crazy though.
Battles would rage on every ocean, and the USN would be split between the Atlantic and Pacific. Assuming Japan pulls off a pearl harbor analog, this is serious trouble for the USA. Furthermore, at this point in history, the US official opinion on rocketry was "children's toys, bugger off." Project Manhattan wouldn't likely be too affected, but we only got ICBM's OTL
after we "liberated" the NAZI scientists who had worked on V1/V2. And while Germany wasn't all
that close to the Bomb, they were closer to the Bomb than the US was to ICBM's.
The time it would take for the USA to build up a sufficient army and Navy to combat the combined arms of the RN and Germany would give the Wunderwaffe a lot more time to be developed and deployed. Most of those weapons were a bad joke, but the Jet Fighters and missile screens would have made strategic bombers almost obsolete (alongside with Britain's tech, we're talking SAM sites vs B-52's!!).
USA would have to knock Canada out of the war first, and occupy it. This is expensive, and not too popular at home. Now, Barbarossa comes into question. If it happens as it did OTL, and Germany had not yet beaten Britain into submission, but Britain capitulates
before Stalingrad, then Germany might have been able to press to Moscow/Stalingrad/Leningrad with forces from Normandy & Africa (plus British forces, especially near Leningrad). That was a close fight OTL... that many forces and that much of a morale boost might help Germany (or not,
supply not manpower was the problem for Germany). If Germany holds off on Barbarossa, then they don't hit an army wrecked by the Purge, they hit a prepared USSR which would be a much tougher nut to crack.
In all, with the commonwealth on its side I'd say the war favored Germany. But actually getting the commonwealth is fantasy. And while Germany might be able to negotiate a peace, Total War with the USA would probably have obliterated the entire northern hemisphere in terms of industry and maybe population if the USA had the same zeal as the Germans/Japanese (I'm not convinced the American public back then was interested in a Total War at home).
TLDR: Brazil wins WW2.