if they had atom bombs, they'd easily be able to take britain. they could take over whatever they wanted in eurasia, then be able to move over the strait to the americas.
you incredibly oversimplifying the scenario
yes, they could capture britain with the bomb, probably even the soviet union. but you can't just nuke everything and still expect what ever you control stay in control. there would be massive revolts in occupied countries, and due to over extention, it would be incredibly hard to take all of them down.
a western invasion would still be a possiblity, with allied control over the atlantic. pushing past teh urals would be handicapped as all of the manpower is being drained there and leave no one to defend the atlantic wall.
and if germany got the bomb first, the us would be second. there is nothing to change that at all. invading the us would still be hell. the industry is massive, almost the entire country has guns to defend themselves with, the navy is huge, etc. plus there would be no possible way to develop enough bombs in time to nuke the hell out of the states.
and if somehow germany pushes past the urals, japan would be out of the fight by then. the us has control over the pacific, and would probably invade the rest of the ussr to gain foot over siberia.
and what year are we even talking about anyways?
