Of course the Finns would likely not be happy with the Scandinavian union and would likely be the Bohemia/Catalonia of Scandinavia. Of course Finland have a Scandinavian speaking minority which was even bigger at this point, so the entire situation may become quite ugly. My guess is that with a politics which favour Scandinavian speakers from 1850, we will likely see a third of the population speak Scandinavian by 1900, but it will likely not grow from that point, and there will increase push for autonomy or independence, including terror.
The OP states that Scandinavia unites (but not in which precise form) around 1850-1870 or something, so Finland is probably as OTL until 1918.
Nordic, not Scandinavian. Scandinavian is (AFAIK) explicitly a North Germanic Qualification, Nordic, includes Finland and (according to the Estonians, at least) Estonia.
That said, while historically, the Estonians were ruled by Denmark and Sweden, I don't seem much reason, after the development of the Estonian national consciousness, for the Estonians to remain content in this case, any more than the Finns would.
OTL Estonia and Latvia suggested creating a union of the Nordic and Baltic countries in the early 1920's, but Sweden turned it down.
And Finland asked for a union with Sweden in 1940, but the Swedes hesitated until it was too late.
By the way, the name "Scandinavia" is not exact and can (if one wants to) be used for any geographical entity, so we can very well have a united "Scandinavia" that includes Benelux and Lithuania. That is, if the 1920s or 1930s sees a need to include all the small North European countries in a bigger state that would be capable to defend itself against Russia or Germany.
The OTL Scandinavian union failed, since it did not have a real superstructure and the Swedes did not care for Norwegian opinions. Suppose that this is changed after the Danish 1848 war, and the ruling cliques of Sweden, Norway, Denmark, and perhaps even of Iceland (then part of Denmark), decide to set aside their differences and create a federal system, where power is defined for the union, the states, the provinces, and the municipalities, in order to create a lasting union between Sweden and Norway, and have Denmark enter this union.
Language issues could be left outside, since there was no consensus for how a Scandinavian standard language norm would look, so everyone will keep to their own tongue.
Such a Scandinavia could then be reasonably fit for including its small 1920s neighbors Finland, Estonia and Latvia. Lithuania was not as close OTL, but that might have been due to its conflict with Poland, others not willing to be dragged into something.
Getting the Dutch, the Belgians and the Luxemburgers to join is more farfetched, but it would make Scandinavia on par, populationwise, with other great powers, and perhaps hold the union out of WW2, which would be very advantageous for these otherwise occupied lands.