Queen Mary was supposed to have said in response to the abdication crisis "This is not Romania" in reference to Carol II.
The British establishment was almost entirely opposed to the idea of King Edward VIII marrying Wallis Simpson, an American divorcee. It is often said that the British public were much more relaxed, adopting the manta "If she's good enough for the King, she's good enough for us." I am not sure how true that is, historically the working and middle classes were (and remain) much more socially conservative than the elite and certainly anyone of a religious vent would have refused to accept Wallis Simpson as Queen.
Your scenario is to add to that Edward has married and produced a family and has then proceeded to ditch his wife and children and wants to marry Wallis Simpson a twice divorced American.
Just as a principle it is unthinkable.
Frankly I think any sympathy Edward might have received in the actual scenario is non-existent in this scenario. The elite would have been appalled, the Church couldn't tolerate a Head of the church married to a divorcee, let alone a divorced Head who ditched his wife to marry her so its unlikely Edward could be crowned, I think the masses would have also find it beyond intolerable and his popularity would have completely ebbed away. Think Charles/Diana/Camilla on steroids.
One further point to add, in the 1930s your average Brit thought Edward VIII was a decent sort of chap, his habitual affairs with married women were unknown to the masses. His relationship with Wallis Simpson was portrayed as a love story.
In your scenario, he has ditched his wife and mother of his children to marry her.
There is no way to try and tidy up that and make it acceptable.