Woah, slow down, I think you're getting your wires crossed. Christian Frederick was heir to the Danish throne and became Christian VIII of Denmark but he wasn't in a position to ever accede to the Swedish throne, especially once the Riksdag had agreed Bernadotte would do as an heir for Karl XIII.
Now consider this: Bernadotte was a highly successful marshal of Napoléon, one of the strategic minds who devised the plan to beat his former emperor in 1813, he carefully husbanded his troops during the campaign so as to not spill one drop of blood more than was strictly necessary, and he then turned those highly trained troops on a very sparsely-populated country which had not been independent (though it had been autonomous at times) for centuries and could not match him men for men. If you check, most of the battles ended in small Norwegian tactical victories and it simply didn't matter because the Swedes could just ignore them and power through: the shooting was over in barely three weeks. In Norwegian terrain, that's tantamount to saying there was no effective resistance to professional troops marching and occupying the country.