Seriously, for that short amount of time, go on a tour, yes you will do a lot of countries in a small amount of time if you so choose one of those 12 countries in 14 days tours, but you will get an idea of where you wish to go back to again in the future. Also you know that all your accommodation & some meals are paid for, you can also ask in advance how much the extras are, like side trips, special meals, have that all budgeted for before you leave, so you only have to worry about spending money.

I've done about 5 tours of Europe over the last 25 years, as well as travelling to different places via car/train/bus/hitch-hiking.

For a Scandinavian visit, I suggest a tour, too expensive otherwise.

Our family did 3 months in Europe when the others were young (11 - 6 in age), I wasn't with them the whole time as I was in and out for work, but they stayed in camping grounds a lot of the time that had these amazing tents, that were almost like cabins, we also stayed in home stay type of accommodation as well. We had the 7 of us in a car, 6 most of the time as I was more inclined to fly into whichever major city the rest of them were at to spend some time with them. The kids were out of school for this 3 months and they were home-schooled during that time, with their school giving them the work they needed to cover.