If Edward doesn't meet Simpson thats a pre-1936 POD, meaning he could have become King sooner or later depending on his father's ailing health. Also no Constitutional Crisis has major butterflies, much more than simply a different bride.
Stanley Baldwin wouldn't step down and unless he cocks up (remember he's just won a landslide election for the National Government) I can't see him being ousted before an alt-WWII breaks out, combination of his politicking and the growing spectre of war would keep him in place. His only real rival was Chamberlain and they were allies more than anything, though Neville's calculating nature and his advancing years might see him go for it.
How Baldwin would deal with the coming of war is tricky. He was adament for peace but during the national euphoria after Chamberlain returned from Munich with the 'piece of paper' Baldwin said he admired the PM's courage but said he himself would not have gone. Also he believed Churchill was the man for a war Prime Minister back in '35, so maybe he would stand aside when things kicked off?
Regardless when it comes down to tanks and bombs I doubt he would have been anymore prepared than Chamberlain.
All this about Edward forcing peace, I really doubt it. I'm not totally up on the subject but bar the infamous hitler salute and a vague support of 'dynamic' political reform I've not seen anything to suggest he was openly pro-Nazi, his constitutional limitations aside.
Right, well Wallis met Edward in 1931 but she didn't replace Viscountess Furness as his mistress until Jan. 1934 when she went to holiday with family and Wallis stayed to 'keep him company'. Scratch that let's say in a fit of passion the Prince of Wales jets off with Furness, seems like his style. I have no doubt he and Wallis might have done a big of canoodling but this is the period they fell for each other. Instead on his extended holiday for falls head over heels for Furness and she stays his girl (he certainly had strong feelings for her so not unlikely). Then we have Wallis shoot off with some other young bachelor.
Minor butterflies will take place but it wont be major, until the point one of them has chance to be Queen, I can't see opinion of Edward's galavanting being too different for Furness or Wallis bar royal circles having more time for Furness. George V might be less stressed over Furness but he had strong moral convictions, relations outside of wedlock was a big no-no regardless of who was involved.
Butterflies will effect the King's death however but I'd say a window of Nov. 35 - Mar. 36 is reasonable, he was very poorly in his later years and flu season was what saw him off. Say March 1936.
This where things get trickier. Edward still upsets plenty of establishment figures by ignoring traditions but Furness will be a much bigger improvement in terms of the State's fears. She won't have anywhere near the dominating effect Wallis had on Eddie so fears of national security and being compromised will be gone. However we're still looking at a controversial divorcee. Best bet to have Baldwin agree will be for a morgantic marriage, barring any children from taking the throne. There were also plans afoot IOTL for a civil ceremony to avoid religious problems but that seems even more radical than allowing a CofE service, don't see the Defender of the Faith getting away with a secular wedding!
It will be under duress but the simple fact Edward VIII stays will be a victory and alot less stressful for the PM. So Baldwin definately stays, though Hertzog the South African PM might kick up a fuss over the issue, being even more hardline than Baldwin IOTL. Excusing the extra burden it will give SA-UK relations in the future not much difference.
Fast-forward to Anschluss, same as IOTL. Then the Sudetenland... hmmm, Baldwin quote saying he would not have the 'courage' to go to Munich bearing in mind his wish for peace and the positive public opinion on the move in OTL makes me think he might stand up for the Czechs. His views on Germany and War are complicated but I basically think he was pro-peace but not the idealist Chamberlain was. I'd imagine Eden remains at FO and with his confidence in Churchill as a future war leader, I think cynicism and the escalation of tensions by 1938 could see Baldwin doubt Hitler's sincerity all not without raging arguments in Cabinet.
Add to that Daladier, if he still becomes French PM after the fall of the Popular Front, a series of events I think would have happened pretty similar to OTL given the short period following the major POD of Edward and Furness' coronation, he will be far from an appeasement voice. French foreign policy relied on British agreement in this period, Daladier hated Hitler but was unconvinced France could go it alone so gave into Chamberlain's passionate support for appeasement. Here, a chaotic British Cabinet combined with French opposition to a deal might tip Baldwin to stand up for Czechoslovakia.
Then its up to Hitler what happens next. Munich gave Hitler the confidence to invade Poland but that was even despite an Anglo-French promise of support to Warsaw after the German takeover of Bohemia-Moravia. Will his free ride into the Rhineland and Austria combined with a tepid British PM convince him to risk it? Refusal to negotiate combined with continued Nazi postering will almost certainly see rearmament being kicked into high gear in the Allied camp. This too might make Hitler risk it, knowing his military machine will be eventually overtaken by the combined power of the world's two global empires. Also unlike Poland, the Sudeten Germans might be seen in Berlin as a guarantee of popular opposition to war in Britain and France.
In the name of interesting alt-history let's say he decides to go for it in spring '39. In the meantime he'll be looking to Poland and Hungary as possible allies to seize territory they've been looking at for years. Maybe Hitler is desperate to use a coalition invasion to shows its merely dismantling another creation of Versailles. Hungary's cause will be particularly well fought for, the Daily Mail under Lord Rothermere was extremly pro-Hungarian irrenditism.
Regardless if he can Daladier will fight for the Czechs and by this point Baldwin will probably have accepted the situation. Germany attacks, making used of the Austrian border to partially bypass Czech defences. Hungary may well go for it though Poland is a lot less likely given their small-ish claims and ties to France.
So German forces cross the border on March 1st 1939 along with Hungarians forces attacking Slovakia from the south. The Allies give an ultimatum, its rejected, they declare war. Stating health reasons and the need for unity (all this wrangling over war will have compromised Baldwin with the doves he was once apart of), Baldwin stands down for Churchill to take his place at the head of a War Cabinet, including National Govt, Labour and Liberal politicians.
How things go will be intriguing but military history is my weak point. I'd say the Soviets would take advantage to press the Baltic States and possibly Bessarabia. Poland I'm not sure about, will probably stay neutral and see how the winds go. If they side with Germany and then things turn sour I wouldn't be surprised to see the Soviets make an ad-hoc deal with the Allies and roll into Poland.
Anyway thems my thoughts on the idea.