Out of curiosity, when will you be taking your trip?
I'd plan 21 days in winter very different than 21 days in summer.
You've been given some great advice and possible routes, but what type of thing do you want to see/do? Do you want Italy for food, beaches, hiking, museums, all of the above? In Switzerland, do you want the Alps, cities, villages, scenic drives? There's a lot to see in each of those countries and depending on what you want to do (and when you'll do it), you'll get different suggestions.
On past trips lasting about 2-3 weeks, we've changed city every 2-4 days. In my opinion, 2-3 days is not enough time to get settled. Obviously it depends on the size of the destination (a small town might not need as much time as a big city), but personally, I'd try for 3+ days in a bigger destination or one I was really excited about.
Remember that long train journeys or flights will take up most of a day and you might need a recovery day or two built in - you'd take a break at the weekend from work/school at home, you might want a day off from three weeks of sightseeing.
If you don't hit all your destinations, you can always go back. ;-) Europe's not going anywhere.
Your second honeymoons sounds like it will be wonderful! Congrats on 10 years!