Interesting thread.
I agree that a different outcome of Napoleonic wars would be significant. If "just" a different peace agreemnet, i.e. Sweden not getting Norway (because Russia doesn't get Finland, bacause...), then the Union is probably going to last for the rest of the 19th century but I agree that it will have to be in a looser and/or mor equal form if it has to live through the 20th century.
If however the OTL isolation/blockade of Norway from 1807-1814 is Pod'ed away, when the British robbed most of the Norwegian and Danish merchant fleets and Norway starved, then I think the Union will have a much better long term survival chance.
In OTL the isolation and the shortlived Norwegian independence in 1814 IMO was the birth of Norwgian nationalism. If combining the PoD'ing away of this event with a political proces giving Norway a more equal position in the Union, then the chances of the Union are drastically improved. The political process could be promoted by the Danish-(mainly) Norwegian merchant fleet continuing the very profitable period before 1801. The PoD could be the British failing to dissolve the Neutrality Union with Russia, Prussia and Sweden. The underlying PoD could be Nelson actually following orders at the battle of Copenhagen in 1801 and the British withdrawing(loosing). If UK ends up seriously pissing off Russia, Prussia, Sweden and Denmark-Norway while also being at war with France, the Napoleonic wars will have to go very differently - so much that a lasting Danish-Norwegian Union will risk ending up as one of the very minor PoDs!
BTW concerning nationalism of various nations we in general have to be very careful, as the nationalist movements of the 19th century usually were very productive in interpreting earlier events as nationalistic in the 19th century sense. A more sober view will see that they very rarely if ever were.
Regards
Steffen Redbeard