I think you have to assign some priorities. If you were an Italian resident planning a trip to the U.S., it would not be convenient to see Boston, Miami, Grand Rapids, and Disneyland in Anaheim on a very short trip such as the one you are planning.
Likewise, you are planning a trip that takes you across long distances in Italy. If you rented a car in Venice, you would probably spend 8 to 10 hours traveling from Venice to Anzano, and would be in the middle of rolling hills in an area not known for its tourism or services for tourists.
Some distance checks: Pisa is at least 2 1/2 hours from Rome by train. If you rented a car in Rome, after factoring in the time to rent and return the vehicle, you are probably looking 5 1/2 to 6 hours, each way. From Rome to Agnano by car is at least 3 1/2 hours each way. Train would probably be easier, but the trains are not frequent to the area of Puglia, so the waiting times would be killer. Venice to Pisa is 5 1/2 hours by car and almost 4 hours by train.
You will be in transit for agonizingly long periods of time, a surefire recipe for having the kids view this as punishment, rather than a vacation. Your original plan is the most feasible, and it takes into account the kids' enjoyment at seeing a tower that leans, and still gives you two great destinations to visit with numerous sights and experiences to enjoy.
I recommend having your husband inform his relatives that he will see them next trip because this one will be too short to make that leg of the trip.