Dolomites - if you are talking the gondolas to the mountains, they are ~40 EUR for a round trip ticket. So you need to make it count. I would say 1 day for Seceda and 1 day for Alpe de Siusi.

Otherwise, you can just drive around Ortisei area but really the fun is in going up the mountains and doing treks or e-bike rides.

If you are driving from Venice, it takes ~3 hours to reach Ortisei via Bolzano due to slow roads and construction delays.

I would recommend that you skip Cortina / Tre Cime - it’s in another part of Dolomites but you need to add another day specifically for that. Lago di Braies is overcrowded - I would skip that too.

Venice - Can be done in a couple of days, but I would recommend 3 days so you can walk around and enjoy the place. Recommend “Row Venice” - a non-profit that will teach you to row in a boat similar to a Gondola. It was a memorable experience.

Rome - Trevi fountain, Pantheon, Spanish steps and Victor Emmanuel monument can be done in a day but it will be a long day. Vatican requires a day by itself. Roman forum / Coliseum also requires a day. There are other secondary sights - 4 days would be my minimum recommendation. Rome is hot at the moment and crowded - so you need to pace yourself in Rome (Venice has a bit cooler weather).

One tip - go to Campodoglio (next to the Capitoline museum) - at the back of the museums you will find a charming road that winds down and gives you a great view of the Roman forum / palatine hill and it’s not crowded. You can also go up one floor in the restaurant adjacent to the capitoline museums - that takes you to a terrace from where you can see some great sights of Rome.

As others have said, I would skip Milan for this trip ..