Honeymoon in late April-early May

Fly in to Venice, out of Rome
Much easier to fly in to Venice than out of and it’s a perfect place to get over jet lag

Count your trip in NIGHTS
14 nights
Venice 3
CT 2
Florence 2
Tuscany 3
Rome 4

2 nights is really only 1 full day to sightsee
You will need a car for Tuscany
All the rest easily done by train

( I would skip CT and give those nights to Florence/Tuscany and Rome)

FYI-
Avoid the May 1 holiday and weekend associated, and avoid the week before and week after Easter. Take it from someone who has learned the hard way. Italians love their holidays!
Also, shoulder season has disappeared, but it still will be cooler. The CT is always jammed now, as is the AC.
Max out your days/ nights as much as possible. What excites you the most, and what are your interests?
At least three nights in each place , four is ideal.

Congrats on the honeymoon!

Would it be overwhelming to try to fit Rome -> Florence -> Tuscany towns -> Cinque Terre -> Venice into a two-week trip?

Don't mean to be Debbie Downer, but my opinion is "Yes". For several reasons.

With the stess and hectic pace that usually comes with weddings, you'll want (maybe need) to be able to relax and unwind - not just go, go, go.

Each time you relocate, you will lose at least 1/2 to 3/4 of a day. It's not just the actual travel time, but the time spent checking out, getting to the train station, and waiting there. Upon arrival you'll have to get to the hotel, check in, and do some unpacking. Those things all add up to lost time.

Consider limiting yourselves to not more that three locations. Day trips can be made from those without losing time relocating.

Perhaps you can fly into Venice and back home from Rome. And you can pick one other place somewhere between the two. Venice is a great, relaxing, laid back place to start a honeymoon, and the pace in Rome will be get you ready to head back to the regular world.

Love long and prosper.

That seems like a lot of hotel hopping for two weeks. I did a Rome -> Florence -> Venice two week trip a few years ago and it was perfect. You can use Florence as your home base for day trips to the Tuscan towns. I would skip Cinque Terre and save that for another time back to Italy. If you're dead set on seeing Cinque Terre, you can do a day trip from Florence there.

I know the first time visiting Europe is exciting, but take it easy!

Possible to relax anywhere you go, even easy to relax if you choose accommodations in the less heavily touristed parts of a town or city.

Unless you've traveled together enough to know what both of you like and don't like, it's probably a good idea to err on the side of underwhelming rather than overwhelming --- you can always add a day trip or half-day trip, but if your accommodations and plans and reservations are all set, it can be hard to skip a tour or a museum or a move to the next location.

Speaking of skipping, you are allowed to plan to skip any location you wish --- we've spent 400+ days in Italy so far and have purposely skipped the Amalfi Coast, the Cinque Terre, the lake areas, the beaches, and many other popular places just because our priorities are different. If you enjoy your first trip, you'll come back.

Venice to Rome plus one other place in between is an excellent first trip.

Thank you everyone for all the thoughtful feedback and suggestions!
I recognize now that I need to keep it simple instead of trying to visit everywhere, especially in 2 weeks.
It's easy not to factor in all the added lost time due to travel, waiting for trains, checking in and out of hotels, etc. so that is good to note!

14 nights
Venice 3
Florence 4
Tuscany 2
Rome 5

Unless you have a teleportation machine that’s way too much for two weeks, and if they include travel to and from Italy it’ll be more like 11 days of actual vacation, which makes it make even less sense. Stick to one region of Italy. It makes things easier that way. I mean, who wants to be constantly changing hotels. Trains I can take, because those are relatively pain free. Avoid May 1st and Easter, because those are national holidays and things won’t be operating on normal schedules, if at all. So, if I were you, on our honeymoon, on the first trip to Italy, I’d stick to either Tuscany or Rome. Rome, and its surrounding areas, has so much to offer, that can’t even be seen or experienced properly even in two weeks. Believe me, I’ve tried. Tuscany, and to a greater extent, Umbria, are even larger and have a huge amount of things to do, see and experience. Being a very long time traveler to Italy (25 years) and one who’s lived there as well, I haven’t even begun to scratch the surface of things to do and see.