We plan of flying "open-jaw" into Roma and out of Milano. We are thinking about staying 4 nights in Rome, 2 nights in Florence our 20 year who is there studying will join us. Then we go on to Venice for 2 nights but then I'm stuck. Will the weather be good enough in mid-April to visit the Cinque Terra or should we just go to a hill town and drink good wine to decompress after all the cities?
I know we are planning an aggressive trip
Venice and the CT are in opposite directions from Florence. If you are going to Venice (3 hours by train), you won't want to backtrack through Florence to get to CT. And vice versa.
So either go to the CT between Rome and Florence, then to Venice, or Rome, Florence, Venice and skip the CT.
In any case that is a lot of hotel changes. I'd stay longer in Florence and take a day trip to Siena.
Also it will take you half a day to get from Florence to Venice (door to door), so perhaps one more night in Venice also.
Verona is lovely. Stop for the day on your way from Venice to Milan. You can check your luggage at the train station. You can do a similar day stop between Florence and Venice, either Bologna or Padua.
I think skipping the CT might be good as well and do add another night to Venice. Remember with two nights you'll only have at best half a day the first and last and the full day in the middle.
You might want to take a look at Stresa on Lake Maggiore. It is not too far from Milan Malpensa and I believe there is a shuttle bus that can be arranged although I'm not sure in April.
The area is lovely.
Yes, the weather will be good enough in April for the Cinque Terre -- just be prepared that it may rain some. A beautiful place is a beautiful place -- even if it rains.
Your alternative is great, too. After how you've planned your first 10 days -- planning 2 days decompressing, in either the CT or the hills -- you cannot go wrong.