Ray's right. If all 4 of you list your priorities along with why they are priorities, you may (positively) find that you all have many of the same things high on your lists or (negatively) find that you don't. At least you would start with a list of some kind, the more specific the better. You all need to list where you want to go and what you want to do/see there.
Is Dublin last on the list because you are flying home from there? How were you planning to get to Dublin from Paris or London if not by plane?
Also heed the advice that people give you about the costs of hitting all the places you list and the time it takes to do that. Although you can't buy tickets there except for trips starting in Germany, use the DB Bahn website to check train routes and times.
For example, I checked for the route from Stockholm to Amsterdam on June 2nd. I picked that arbitrary day because the July information is not there yet. The options varied from 3 to 9 train changes and from about 18 to 24 hours. Compulsory reservations are required for at least one of the trains on each option shown.
You need to drop most of the cities you list if you actually want to see anything besides the scenery between locations and do anything besides stare out the windows. My recommendation would be to drop Scandinavia (Stockholm and Copenhagen) for a start.
If you are set on flying out of Dublin, dropping Paris could also be an option, even though it pains me to say it. If you are not set on Dublin, I'd drop it as well as London and stick with continental Europe. That's still too much for 2 weeks, but at least it puts you within a somewhat reasonable striking distance by train. Remember that the more people there are, the more complicated everything will become and the group will only move as fast as the slowest member of it.
There are lots of ways to approach this, the priorities list being the most important, but you could make a wonderful experience by locating yourselves in 2-3 cities (London and Dublin, London and Paris, Amsterdam/Brussels/Paris, Berlin and Amsterdam -- the combinations are endless) and exploring them and their environs.
This may seem trivial, but one advantage to sticking with the continent is that you will have to deal only in EUR (unless you go to Switzerland). If you were to somehow do all the locations you listed in your question, you would have to use EUR, DKK, SEK and GBP. Unless you are very good at estimating how much cash you will need to withdraw from the ATM, you will either end up with leftovers or have to exchange them at a loss. That might be important from a budgetary point of view.
By the time you go, after your time in Italy, you will be well-experienced with trains, buses and other means of public transportation, so do some research now and trust that you will also learn a lot about European trains in the metal over the next few months.