We did the Northern Europe 7-night cruise in 2016. It was an amazing itinerary. We were traveling with some friends and their 9-year-old son, so we found it was more cost-effective to book private tours for the 7 of us than to pay a per person charge on a Disney tour. I relied on TripAdvisor to find the tour companies and was very pleased with both.
In Tallinn, we arranged a private walking tour with Estonian Experience and loved it. Our wonderful guide, Susannah, met us at the port and led us on a 3-hour walking tour of the old town. At the end of that, she directed the two men in our group to the KGB Museum where EE had already signed them up for the English tour. (They are both history buffs and to say they loved this tour is an understatement.) Then Susannah took the rest of us to a local candy shop where we had a private marzipan molding & painting class. This was very fun – my daughters (ages 12 and 10) said this was their favorite excursion of the trip. They didn't offer the class on their website but when I asked about it, they added it. The owner of Estonian Experience even met up with us at the marzipan workshop to ensure that we were happy with everything. We had excellent customer service from beginning to end, and I highly recommend them. Although our kids were older than yours, I think this would also appeal to younger kids.
For St. Petersburg, we did the 1-day deluxe private tour with SPB Tours. All of my pre-trip communications with them were very professional and positive. Our veteran guide, Svetlana, met us at about 9 am right after we exited the terminal. She was incredibly knowledgeable and worked hard to keep us on-track on our ambitious schedule and ahead of other tour groups. We had a city tour, brief tour of the highlights of the Hermitage, took a hydrofoil to Peterhof, toured the fountain park and upper gardens, had lunch in a local cafe (included in the tour price - even including a shot of vodka for the adults), toured Catherine's Palace, and then finished with a visit inside the Church of the Spilled Blood. They dropped us back off at the ship around 7:30. It was a long, grueling day - especially for the kids - but each of those sights was absolutely amazing. All of the adults decided that there wasn't a single sight that we would have omitted from our itinerary to shorten the day. I had not been that excited about St. Petersburg before the trip, but it really blew me away. That said, based on how our kids (ranging in age from 9-12) handled the day, I would be very hesitant to try that tour with a 6 and 4-year-old.
We decided to do Helsinki and Stockholm on our own. In both ports, we took the free shuttle that Disney provided into the heart of the city. We didn't identify any must-see sights in Helsinki, so we just walked around Market Square and Senate Square for a little while. It was a beautiful day and a very pleasant city, but we didn't really find much to do. We were also still recovering from our whirlwind day in St. Petersburg. My husband took the kids back to the ship to swim and do the Aqua Dunk. I did a little shopping at some of the cool boutiques on the Esplanade and then returned to the ship. Our friends visited the Rock Church, which they said was very funky. In Stockholm, we walked to the Vasa museum. It was a long walk (not recommended for your group), but the weather was beautiful, and it was a great city for strolling. We all enjoyed the Vasa, but I'm not sure it would appeal to kids as young as yours. We wished we had had significantly more time in Stockholm.
When you're in Copenhagen, be sure to check out Tivoli Gardens, which was supposedly Walt Disney's inspiration for
Disneyland. It is charming, and my girls had a great time there. We also did a canal cruise on the first day, which was a fun way to see the city. It goes by the Little Mermaid, so you can say you've seen her without making a trek out there. We purchased the Copenhagen Card, which included admission to Tivoli, the canal tour, transportation, and admission to lots of other sites.