by the 1960s with woman taking a greater role in society that might change, more so since her children, the future king, wouldn't be HRHs, in OTL their grandfather changed that but in this world… well the titles issue would be a nightmare.
In TTL I'd anticipate that Edward VIII would grant the "HRH" style to Elizabeth's children as George VI did in OTL. However, as Elizabeth would no more be Edward VIII's heir apparent in TTL than she was George VI's in OTL, she wouldn't become Princess of Wales. And yes, titles in this world would be a nightmare to sort out.
I think the married with children Elizabeth would enjoy more popularity than the single Edward.
Most probably.