June and September would be probably be quite warm in Sicily. I don't know about May.
I was in Norway, Sweden and Finland (the latter not being part of Scandinavia, I realize) from mid-June till late August this year and was very pleased with the weather. I had a very few days when it went over 80F. There was some rain, especially in Norway, but that was expected. I'd recommend doing some weather research on timeanddate.com to see how recent temperatures and rainfall levels fit in with your idea of good sightseeing weather.
Two weeks won't go very far in Scandinavia if you want to go beyond the capital cities. It's a very large area. I'd stick to one country if I had just two weeks. Think about it this way: What capital city doesn't deserve at least 4 full days (five nights)? Isn't the second city (Bergen in Norway, Gothenburg is Sweden) likely to be worth 3 days (4 nights)? That's well over one week for a single country and you've only seen two cities. You can add a day in Norway and do the Norway in a Nutshell route between Oslo and Bergen without spending the night anywhere along the way, but that's a long, tiring day.
I saw a lot Norway and Sweden (less of Finland due to lack of time) via public transportation, but with a rental car you'd have more flexibility in fjord country. I'd still want to take the Flamsbana from Myrdal to Flam (or vice versa) and the ferry through the Naeroyfjord, but there's much more available if you are willing to explore in your own car.