Agree that you have to limit the number of cities.
You will be exhausted by the end of the vacation.
2 cities a week. The travel is going to be tiring as well as the packing and repacking. With more cities, way too much of your time would be wasted travelling & packing and checking in/out of hotels.
Rome is amazing. You can then do a quick trip down to the Amalfi coast for the beach aspect.
Frankly, I would skip Zurich and Milan.
And the above poster is correct. Britian and Greece are out of the way of the other destinations.
Perhaps you may alos consider Vienna or Prague.