I'm not sure Stanley Baldwin really wanted a National Government, Roy Jenkins (in his biography of Churchill) seems to think that he would have preferred a Tory-only government so as to keep the Liberals in competition with Labour for the centre-left vote. He was in the South of France at that moment on holiday and thus left negotiations in the hands of Neville Chamberlain. At the time most thought that a Conservative-Liberal coalition was the most likely outcome of the fall of the MacDonald Government.
With regards to Churchill being opposed to a coalition, I'm not sure how true that is - Churchill was never particularly tribal and was quite happy to work with certain Liberals. Like other aristocratic politicians of the period he bounced around the centre and right wing of the political spectrum quite a lot during the inter-war years.