E.S.
Hi,
I think your best bet are the hotels on base. Europeans don't have such large families in general even though the Italians love the "bambinis." When you use the hotels on base you might even get a little kitchenette but if everything else fails you have the fridge and a coffe maker. In the European hotels you first have to clear the mini bar.
When you go into Venice I suggest you take the car--even if someone suggests the train but you have 3 paying adults and 2 paying kids. For about 20 Euro/day you can park at the centrally located parking garage and just cross the street and hit one of the Vaparettos--public water "bus" to get to San Marco--the center. I suggest you get one of the day tickets. That way you can hopp on and off them the whole day. It is a very tiering city especially for the 2 little ones. If you can do no stroller it would be easier due to the many steps in Venice and cobble stones or use one of the cheapy light weight strollers that one person can handle over the steps (your older kids) and you carry the little ones. Then there are the 2 islands Burano and Murano. Might be good to go to with your kids as the time on the water will be down time for them. Though Venice is not a city to be seen in only one day anyhow.
We have lived in Vicenza from 03-06 if you need some more info let me know. I still have contact with some Americans in the area if we need some up to date info.
Have fun, go with the flow in Italy, it's a totally different pace when you talk about driving (very fast and caotic) and all other things very slow. Be adviced that most of the stores are closed from about 1-4pm exept Venice. Depending when you travel in the summer it's a bit different anyhow in A. because most Italians take their summer vacation during that month and they pretty much go to the beach.
Now if you only can go in the summer months that's what you have to do and don't loose patience due to the massive amounts of tourists. Hit Venice very early in the morning to get a parking space in the parking garage but if you could do spring or fall vacation it would be more enjoyable due to the fact of less tourists and lower day time temperatues.
Good luck!