Oh yes, seeing St. Petersburg during the White Nights is wonderful!

Stockholm is a must in my opinion--one of the most beautiful cities I have visited. You can take a night ferry to Helsinki: start in one city early evening and arrive in the other in the morning.There is a ferry every day. Check Viking line for this.
Oslo and Copenhagen are more ordinary.

Ferries also go to Turku, on the western Finnish coast and a nice city - then trains take you in a few hours to Helsinki so Stockholm to Helsinki is not the only option.

http://www.siljaferry.com/

Silja runs really nice services IME Stockholm to Helsinki and many other services in Scandinavia and Finland.

I have done home exchanges in Lahti, Finland; Taby, Sweden (suburb of Stockholm) and Fredrikstad, Norway (one hour south of Oslo by train). If you have only 2 weeks, I would hold Finland and St. Petersburg for another trip. With 2 kids you don't want to over schedule yourself and end up with everyone being a grouch. Oslo city is not that interesting, but the Bergen to Oslo fiord cruise and train ride (goes through Finse, which is supposed to be the highest train station in Europe; you might see snow out the train window in summer!). The Finse station is not open off season.

I would fly from Oslo to Bergen, go across to Oslo. Train connections to Stockholm are difficult and you might want to fly. It does depend on how much you want to ride trains. When I did my Norway-Sweden home exchanges (one after the other) in 2012, I found it cheaper to fly than to dither with the train (which required a connection).

To get from Stockholm to Finland, you can take the Silja Line to Helsinki or Turku and rent a car, if you want, after you arrive. The ferry ride is a full day deal. While the scenery is awesome when the weather is nice (lots of islands), there are also amusements for children on the boat that require no specific language so that all can enjoy them. Your train passes might be good on the ferry. Since I never buy train passes (individual fares for me are always cheaper than the pass), I don't know and you would need to investigate. As is true in the US, flying is often cheaper than the train.

I think you need to narrow down your choices and see if you can possibly have more than 2 weeks. Each country in Scandinavia (and, for this statement, I include Finland) is worth more than 2 weeks by itself.

Thanks again everyone, your suggestions are really appreciated. Could you also please suggest best places to stay in Copanhegan, Oslo,Stockholm, Helsinki. As I will be traveling by train, I would prefer to stay as close to train stations as possible. Would really appreciate if you name the area/suburbs.

I have no suggestions as I am always traveling through home exchanges. With all 4 cities in 2 weeks, you will spend a lot of time in transit.

For accommodations, you might check booking.com and use the map feature to see where they are in relation to the trains and major sites.

If you're buying a Eurail ScanPass that pass does or at least used to grant discounts at some major hotel chains in some of the four countries it covers. check out details on the pass info sheet or at www.raileurope.com - originator of the pass and who lists the conditions of use on its web site.

Helsinki city Hall and the surroudning market square is a must stop. Many scenic view points and sights are near by. They had the "flush" exhibit in the city hall while we were there last year, most interesting ...

hetismij2: Is Denamrk Scandinavia? I thought Finland definitely would be ..

Denmark is considered Scandinavia but Finland is not. They are both considered Nordic countries though.

We did the following two week trip in 2011:

- Day 0: Fly into Copenhagen
- Day 1: Arrive early morning in Copenhagen, full day of sightseeing
- Day 2: Copenhagen
- Day 3: Copenhagen in morning/afternoon. Evening ferry to Oslo
- Day 4: Arrive in Oslo early morning, full day of sightseeing
- Day 5: Oslo
- Day 6: Norway in a Nutshell (Oslo->Bergen via train/boat/bus)
- Day 7: Bergen
- Day 8: Fly to Stockholm
- Day 9-10: Stockholm
- Day 11: Fly to Copenhagen. Afternoon in Dragor.
- Day 12: Fly home!

Hectic but fun schedule. If you have extra days, add them in Oslo and Copenhagen.