I will be in Norway July 20-26, then 2 days in Stockholm. I have been ready some of the negative reports from some travelers who experienced problems with train cancellations and large crowds. I do not need to complete the tour in 1 day and can stay overnight in Bergen or maybe Balestrand. Would it be best to take the train from Oslo to Bergen and use that city as a base for the tour? I am concerned on handling the luggage between train, bus, and boat.
I am seeing mixed reviews on the train between Mydal and Flam. Are there problems with the connections on this train?
First, if you have the time, doing the Nutshell tour over several days is certainly more relaxing than taking the overnight train back to Oslo from Bergen. Bergen is worth at least a day of walking around. Regarding baggage on the tour. You should ideally limit your baggage to a single easily manageable carry-on because the train-boat-bus is not conducive to "checked luggage". We did the Nutshell ahead of a ski tour and solved the problem by leaving our skis and ski gear as "checked luggage" at our Oslo hotel. We did not have connection problems. To the contrary, the modes of travel seemed to coordinate (when we did it some 10 years ago).
I'm not familiar with the Norway in the nutshell tour, so I'm not sure which cities you're planning to visit. If you have time, you should visit Stavanger from july 25. A large food festival called gladmat (happy food) is a tradition in Stavanger, and serves amazing food in the harbour. If you decide to travel to Stavanger you should also experience the pulpit rock. Though it's sort of time consuming, so you might not have enough time.
I would second the comment that NiN should not be done in a single day. There's too much to see in that time frame and Bergen is worth a visit. You cannot do that with luggage in tow. If you were REALLY going to do it in one day, then I would leave my luggage in Oslo and do it. Otherwise, stop and stay overnight and enjoy your time in the fjord instead of worrying about making your train connection back to Oslo.
I don't think that the Flåmbana is going to be a problem.