So if I am wrong please correct me, but I assume the larger question, is why was the US fighting Germany with the Allied Powers to begin with?

Its easy to understand why the US went to war with Japan after tensions and provocations on btoh sides boiled over with the attack on Pearl Harbor. But Germany is indeed a different beast.

In short we can point to a host of factors that came together, and FDR's role as a pivotal actor in shaping US policy. He simply didnt expect anything but the worst from Hitler's Germany. He saw them as expansionist agitators who would do anything but contribute to global stability and who would be unsatisfied with simply dominating the European continent. While he saw the Allied powers as defenders of "liberty" and democratic ideals being sorely beset, along with natural inclinations towards siding with former allies from WW1 against the same foe again. In fact for months before the entry of the US into the war the Army and Navy had agreed in principle to focusing on a "Europe First" strategy that placed Germany as the more immediate foe that must be dealt with. This was made policy in what is known as the "Rainbow War Plans" specifically Rainbow 5. Then in secret meetings with Churchill(at the ABC and Atlantic Conferences in the Spring of 1941 before US entry into the war). The US and UK then issued a joint statement known as the Atlantic Charter which unequivocally placed the US as backing the Allies, which backed ideals such as denial of territorial gains by aggressor nations, and self determination, and was meant to really define the ideals behind the sizeable material aid that the US was providing through Lend-Lease and similar deals like giving the Royal Navy 50 destroyers for use of British bases in the Western hemisphere.

The Nazi Govt did not take this lightly of course and in the weeks before Pearl Harbor U-Boats and US Navy ships escorting convoys to the mid point where they would meet British escorts were in a shooting war even if officially not at war. While the US had also aided the Allies by other moves such as taking up the task of placing a garrison in Iceland to free up the British troops that were there. However in the aftermath of Pearl Harbor it was an issue of intense concern for the US govt about what to do about Germany as there was still little initial will to take the leap into war with them. The Hitler did the US a favor by declaring war himself on the 10th, thinking the US a weak and unprepared nation already against him and in solidarity with Japan.

As for invading Northern Euorpe, the US actually initially wanted to invade much earlier in 1942 or 1943. However Churchill and the Britihs convinced them to have a few warm up fights essentially. Hence the landings in North Africa in late 1942, then Sicily and Italy in 1943-1944. And only then in part because Stalin would let the issue go no longer(he wanted as many other threats drawing German forces as possible), for mainland France in summer of 1944.

There are many wonderful single volume histories of the war and larger series of course. But for a great examination of the US at war in Europe, I would suggest the trilogy by Rick Atkinson. It focuses on the US in the war in Europe but does give goo context, and won multiple awards including the Pulitzer. It begins with An Army at Dawn. Both in depth, but also full on personal stories to provide a face to war and very easy to read.