If you decide to drive, be aware you will need the following for the drive to Venice:=
All drivers in Austria and Italy require by law an IDP - International Driving Permit - which will need to be used with your home license if stopped by police or in case of an incident. You need to get the IDP before you leave home.
You need to budget time prior to the Austrian border (or you can get before leaving the Füssen area as it is on the border) to buy and stick on the windscreen in the correct place an Austrian Vignette. It is instead of tolls on the Austrian highways and tunnels. It costs around €10 for 10 days and both automated cameras and police in cars and on motorcycles will be checking - if you don't have it there will be a big fine. If the actual police stop you it will need to be paid on the spot; if the cameras get you it will come in the post; if they both get you it will be both.
You need to budget for the high toll (in addition to Vignette) at the Europabrucke (Europe Bridge) south of Innsbruck just before where the highway enters Italy.
After the Europabrucke the road steeply goes downhill. This is a danger area for campers, caravans and other trailers and in two of my journeys through there I had longish delays when one flipped. I'm pretty sure that there is a reduced speed over the brow, and I think that TUTOR is in that area.
You need plenty of cash for tolls because all the way to Verona, and all the way from Verona to Venice you will paying tolls.
Be careful of your speed in Italy, even if others around you aren't. They have instant acting speed cameras which will send you a ticket in the mail, and the locals will know where they are and you won't. There is also TUTOR which measures your average speed over a long distance such as 10 km. If you've exceeded the limit you'll get a ticket in the post.
There tends to be a wall of trucks in the slow lane as you approach the exit for Mestre and Venice. Use your phone or a good GPS to show you the exit you need because you may not be able to see the signs. If you get to the toll booths before the airport you've gone too far. Yes, this is the voice of experience, and I drive my personal car from home to Venice most years.
Be particularly careful of the speed limit on the Ponte della Libertà, the bridge linking the island to the mainland. We have seen reports of tickets arriving for just a couple of km/h over.
Some higher value cars are not permitted by certain car hire - rental - firms to go into Italy. You should disclose when you get the car which countries you are likely to take the car to.
If you should be tempted to go a little out of your way and drive the Fern Pass expect delays.
You asked
Drive and park at hotel for the complete stay.
There are no roads in Venice. All cars must either remain on the mainland or park at either P Roma or Tronchetto and then you get around Venice by boat.
I'm glad that you are taking the time to see Venice, my favourite city in the world. It is completely unique and absolutely worth the experience. I know that you are tight for time, but once La Serenissima makes you fall in love with her you won't want to leave so soon.
I hope that you have a marvelous time..