If there's enough discontent in Britain with Ernest Augustus, might there be public pressure for him to abdicate (on behalf of him and his descendants), making the liberal Duke Augustus of Sussex king?
That's a great PoD! If that did happen, a scenario could be:
1) Sussex refuses to take the Crown unless his marriage is recognised and his wife becomes his Queen.
2) Parliament tells Sussex no, he can be King but he can't have the Queen he wants.
3) Sussex renounces his succession rights on condition that his wife will at least be recognised as HRH The Duchess of Sussex.
4) Parliament places the Crown on the head of the Duke of Cambridge instead. King Adolphus recognises his brother's marriage. His son George is created Prince of Wales.