Helsinki, Stockholm, and oslo any maybe copenhagen with a 5 year old

Suomelinna won't take an entire day. You may want to combine a trip to the zoo, as the boat dock for each are pretty close to each other. The ski jump in Oslo is no more impressive than any other in the world. The only reason to go here at all is if you're a huge fan of the sport... and maybe for the view if affords of Oslo. If you're at the Norse folk museum anyway (if the kid likes animals, this one will be a hit), you may want to combine it with one of the other nearby museums. A 5 year old will probably find the Viking ship museum boring, but might enjoy the Fram Museum, because you can walk through the ship.

Thanks for the tips

Looking at your itinerary, I think you've added unnecessary travel to the mix starting at day 11. Do you have to start the cruise at that point in AMS? If possible, I would cut out the back tracking to give you more time on the ground. Not knowing anything about the details of your cruise, this would be my dream rearrangement: Day 1 - Arrive Amsterdam (I am assuming you have R/T tickets to AMS) Day 2 - Amsterdam Day 3 - Amsterdam Day 4 - Fly to Helsinki from AMS Day 5 - Helsinki Day 6 - Helsinki. (OPTIONAL: Depart at 17:30 by boat to Stockholm) Day 7 - Stockholm. (EITHER: Arrive by boat at 9:45, if departed by boat on Day 6 OR: Fly to Stockholm) Day 8 - Stockholm Day 9 - Stockholm Day 10 - Stockholm Day 11 - Oslo Day 12 - Oslo Day 13 - Norway in a Nutshell to Bergen Day 14 - Bergen Day 15 to 21: Hurtigurten to Kirkenes. Day 22 - Kirkenes. Fly to Amsterdam (THIS may be tricky and would be the wrench in the plan. No flights on Saturday, but Norwegian.no has OK prices. SAS is pricey! If need be, you can add a day in Kirkenes or Bergen at the begining to make it work) Day 23 - Amsterdam
Day 24 - Depart AMS to US The variables would be the price of the cruise, whether you've already booked it, and the price of getting back from Kirkenes. Another alternative, if it is cheaper is to fly to Kirkenes first and then take the Hurtigurten down from there to fly from Bergen to AMS. Just a thought, if that is at all possible.

The cruise leaves out of Rotterdam and is already booked so we can't changed that plus we fly in and out amsterdam so we're stuck with those as being unchangeable.

The cruise leaves out of Rotterdam and is already booked so we can't changed that plus we fly in and out amsterdam so we're stuck with those as being unchangeable.

Speaking of Rotterdam, here's something for the 5 year old- Trainz Miniworld. It isn't as large as the more well known Miniatur Wunderland in Hamburg, but it's still impressive. You will find it very close to Rotterdam Centraal. If the kid likes trains, also consider a day trip from Amsterdam to Utrecht for the Nederlands Spoorweg Museum (Dutch Rail Museum). Very, VERY kid friendly.

Helsinki has a great zoo on an island, you take a fun little boat ride to it. The overnight ferry goes between Helsinki and Stockhom and is a nice change of pace over flying. I took the Silja lines ferry and had a great time. I booked through a travel agent and the price was actually less than online from the cruise line (less than 170 euros for 2 adults in August). In Stockholm, the Skansen is awesome. Tons of great stuff, especially for kids. This could occupy quite a long part of your day. I am not a huge fan of Amsterdam, but if you take a train out of the city, you can go to zaanse schans which is a fun take on the traditional dutch life/crafts. Fun stuff for all to see and explore there, from wooden shoes to cheese to windmills.

Those are good suggestions