Skipping part of the Nutshell

Personally I would take the Hurtigruten from Bergen to Alesund.

Coastal views are nice, but I'd say they are somewhat different from the view of the Naeroyfjord you'd see from the Gudvangen-Kaupanger ferry (or the Gudvangen Flam ferry). In addition, if you travel northbound on Hurtigruten, it's an overnight trip from Bergen to Alesund. True, days are very long in June, but will the traveler be awake all that time to see the coastline?

I've only traveled in Norway via public transportation, so I can't comment on the proposed driving route. However, I recall some earlier posts about driving from Bergen or the Sognefjord area up to Geiranger. Perhaps you can find those via the Search function. Specify "forum".

First check the costs for one-way car rentals which can be expensive in Norway.

Are you sure you can even drop off a car in Gundvangen?

I think the intention is to keep the car all the way to Alesund.

I think this is a great idea! The fjord cruise (where you can bring a car) from Gudvangen to Kaupanger is really nice, and Solvorn is such an idyllic place. After that you could drive through Fjærland to visit the Glacier Museum and see the Bøyabreen Glacier arm.

Gudvangen-Kaupanger is a private car ferry which is only operated around summer months - not part of the Norwegian street network such as other state-operated ferry lines. Reservation is really recommended when traveling with car.

Yes, my intention is to keep the car. The cost isn't really much worse than figuring out other transportation for three people. I have signed up to be notified when you can reserve the ferry.