Car rental vs. Rail pass

Once you add in diesel, highway tolls, parking and most importantly the added stress of finding your own way, the cost and convenience of trains and airplanes may be more evident.
Cars have an advantage if you are carrying lots of gear, traveling outside of cities and really know the area you are visiting. Good maps and GPS help, but don't often help you with knowing when traffic is heavy or about construction. For example, if I put an address into my phone at home, I will often not follow it because I know my city better than my GPS apps does.
My suggestion would be to rent a car to go to smaller places you are looking at, return the car and fly down to Rome.

Renting a car in Prague to go to Rome would be rather expensive since you can't rent a car in Rome with Czech license plates. Thus you would, in effect, pay to have someone drive it back to the Czech Republic.
A rail pass would be a waste, IMO. Just buy rail tickets. You could inexpensively travel to Krakow by rail, then fly to Rome, or elsewhere in Italy and rent a car there if it makes sense to have one, such as touring in Tuscany.

Fly from Prague to Venice on Wizzair. Venice is a wonderful place. Take high speed train from Venice to Rome for dirt cheap if you buy the train tix in advance.

Renting a car in Prague and dropping in Rome would incur an enormous foreign country drop fee.

Consider renting a car in Prague to visit Kraków and Seldec and returning the car in Prague. Then a short flight to Rome where you can take train, bus or car to Orvieto, Assisi or many of the smaller cities and towns before returning to Rome for the remainder of your stay. Flying to Venice on Wizzair is a great choice because it's quick, inexpensive and you can see La Serenissima. From there, train connections or car rental is reasonable to visit many of the extraordinary cities on your way to Rome. Depending on what you want to visit in Italy, the "break even point" between car and train tix for four should be about equal but the convenience of the car might win out.

Traveling by public transport does not preclude visits to Kutna Hora or Krakow. Prague-Krakow is served by a direct overnight train or faster morning (7:45) departure with only one connection.

If you were to drive to Rome, where do you want to stop and visit? If you were to take the train, will the stops be the same, or be defined by the fastest train route (via Munich, Bolzano, and Verona)?

As the posts above indicate, it's not a binary choice of rail pass or car. There are also the options to take a flight or bus for certain legs, and if you are taking trains, pre-booked tickets can often beat the cost of a rail pass these days.

If you are looking at trains, the famous rail guru The Man In Seat 61 has two pages you should read. First, here's his great discussion of the issues around rail passes these days: http://www.seat61.com/Railpass-and-Eurail-pass-guide.htm#Should%20you%20buy%20a%20railpass%20or%20pay-as-you-go

And here's his list of which websites to check for the cheapest advance purchase tickets for each place. Make sure, when comparing prices, that you use these links - not Rail Europe or any other source: http://www.seat61.com/Europe-train-tickets.htm

Thank you all for taking the time to help me make this very important decision.
I think we may have come to a decision in no small part do to all of your excellent advice.

It looks like point-to-point tickets are going to be the cheapest bet for us. Krakow will have to wait for another lifetime. We haven't committed to any other cities yet but it looks like we will be heading to Vienna for a couple night and then somewhere away from the cities for three nights before capping it off in Rome.