What sort of luggage will the three of you bring?
You should not consider using the boot/trunk of your car as a mobile secure locker because cars in tourist prone areas tend to be break in prone. When you stop for the night you should take your luggage in with you.
I ask what luggage you will be bringing because the boots/trunks of European cars tend to be quite small. My family sized car with seats for 5 only holds 2 carry-on sized bags with a few soft carrier bags and a few maps. Or one full sized suitcase and a couple of soft bags and some shoes.
If you get a small car it is likely to be manual transmission, with a very small boot.
Expect to pay plenty more for a large enough car with automatic transmission, and more if you want air conditioning. If you want GPS it will be quite a lot to rent, or you can bring one from home which has European maps on it, but be sure to clean the windscreen where the sucker was or every thief will know you have one that is easy to take.
Remember for your long trips that the cheap fares (well in advance) on trains will be on trains with comfortable big seats and large picture windows (except the Eurostar which has comfortable seats but relatively small windows) that can travel between 300 and 360 kph. You will be doing only a maximum 120 in Netherlands, Switzerland, and Belgium, 130 in Italy, and even in Germany which has no limit on some autobahns you will be expected to keep to 130 because your rental won't have high speed tyres/tires.
No way you can keep up with 300 kph. If you take the train you see more because you arrive sooner,
All of those figures are maximums because there are automated "automatic number plate recognition" cameras which monitor speeding not only at the location where they are but often averaged over much longer distances as well which send you tickets months later.
They are also maximums because - like the poster above said - the traffic very frequently and regularly grinds to a halt. Many of the motorways are only 2 lanes each way so when you get to a hill and a large heavy truck pulls out to overtake one going just a little slower (they have computer controls on the engines restricting their speed to the much slower truck speed) it can sometimes take 10 minutes to clear because it is only a tiny bit faster and you all slow down to 60 kph or 100kph or something silly like that.
It is a little different than US freeways.
You will want to be sure you pay a little more to rent a diesel car (but be sure to use the right hose - the colours are different in European countries - and know what diesel is called in each country) because it is much cheaper to fill up and mileage is better. Still very expensive by US prices though.
If the 3 of you still think it is a good idea to drive 4 or more hours each way for a day trip to Venice, dealing with traffic around Milano, Verona, Brescia, Vicenza and Padova before fighting the wall of trucks for the exit for Venice - and then what will you do with your car - instead of a comfortable train from Como S Giovanni with one connection in Milano Centrale which takes 3 hours and a touch right to the side of the Grand Canal - you won't believe the view - let me know.