In short, the Russian Empire, the UK and Prussia would not permit it. Sweden-Norway would have no problem beating Denmark, but Russia would not allow any one power to control the entrance to the Baltic Sea, in addition Russia would not allow Sweden to gain power which could increase the risk of it going to war with Russia to regain Finland. Thus Russia would most likely interveen, in such a war on the side of Denmark, or at least stop a war by threatening to do so, as they did to Prussia in the First schleswig war. The UK did try to pervent any changes in balances of power in Europe during this period, so they would probably try to prevent the rise of a new great power in the North, and Prussia would also probably prevent the rise of a new great power on their Northern boundary. In addition, during this period there was a very strong Scandinavianism in Norway, Sweden and Denmark and strong cordial relations between their peoples, so a attack on Demark by Sweden would probably be viewed very negativly by the people of Sweden and Norway. Rather there were calls to aid Denmark against Prussia, and there were Norwegian and Swedish voulenteers on the side of Denmark.

Short answer: it couldn't assimilate it or keep it.

Even if nobody opposed it, like Zenkappa point out, one should keep in mind that Norway was an integral part of Denmark for centuries and Denmark and Sweden were fighting each other often and became rival so Sweden had issues keeping it and eventually lost Norway because its population didn't want to be Swedish.

Sweden did manage to conquer and hold another Danish land, Scania, but only by oppressing and murdering the Danish population there into submission and assimilating them by force. As you'd imagine, that's harder to do with the whole of Norway AND Denmark which put together have traditionally more population than Sweden. It was much easier for England to do all of this in Britain and Ireland because England is very big compared to Scotland, Northern Ireland, Wales, both as territory and population (and it still failed to completely assimilate even those and will most likely break away).

Sometimes it's better to take small bits rather than choke on something big but the small bits that they could have taken: Greenland and Iceland were not worth it from an economic point of view, they literally had no advantages at the time and even Denmark tried to trade Iceland away at one point. Great Britain would also very likely feel threatened by this move since it would mean that the GIUK gap could be potentially exploited by a fairly powerful European country against it.

/u/Zenkappa and /u/Yawnwarmachine claims are in large correct.

BUT, If Sweden would had joined the war it would had been in accordance with the Swedish-Danish defense alliance that never became. The hope of the two kings, as i understand it, was that this alliance would be the first step towards joining the kingdoms into one Scandinavian nation. This had happen just before in Italy and was about to happen in Germany. Swedish troops also did arrived in support of the Danes, some were stationed in defense of Copenhagen, some died at Dybbøl.

The Russians, English, French and Germans would not allow this, so it was all a fantasy. Had the Swedes joined the Crimean war on the side of the English and French, as asked to, it might all have been different. But to argue about a Swedish invasion of Denmark is in my opinion incorrect.

Hedin, E 1953, Den Skandinaviska Alliansfrågan : 1857-1863 Intill Ulriksdalskonferensen

Hellstenius, M, Krigen Som Inte Blev Av : Sveriges Fredliga Officerskår Vid 1800-Talets Mitt, Lunds universitet, 2000