Prague, Autschwitz and Slovenia

It seems like all three of your destinations are far from one another...are you wedded to seeing them all on this trip? For one thing, it would be a shame to go to Auschwitz and not have any time to see Krakow, especially since it's out of the way from most places (and it's an incredibly lovely place). It's over 7 hours on the road from Prague to Krakow and that's only one-way (train would be longer and I'm not sure about availability of direct flights). With 10 days, I'm not sure I'd suggest zigzagging across three countries that are rather far apart - it seems too inefficient.

At any rate, Polski bus would be a very inexpensive option...but it does take 7 hours 25 min. You'd pretty much need to build that into your schedule, as well as a very likely overnighter or two in Krakow. Do you have enough days to do this?
http://www.polskibus.com/en/index.htm

You might want to prioritize your itinerary and make some adjustments. Traveling your itinerary is just not efficient or close together.
Slovenia is south of Vienna and east of Venice. Have you considered packaging it and Budapest together? Budapest and Prague are cities that are somewhat alike. Slovenia also has some very eye opening WWII history, too.

Have you been to northern Croatia/Istria area? That pairs a lot better with Slovenia and cuts down on transit time.

Instead of Auschwitz, Mauthausen Concentration Camp is more directly along your route, either as the crow flies or the car drives. The best train schedule from Prague to Mauthausen is departing 9:30 a.m., 5.5 hours with one connection at Linz, which doesn't leave you much time at your destination. A private shuttle van would be a better plan, taking about 3.5 hours. Car rentals can be much more expensive if picked up and dropped off in different countries.

Terezin camp is a day-trip option by bus from Prague, but wasn't and isn't the same kind of experience.

We drove from Prague thru the lovely Tatras as Rick recommends seeing, saw Auschwitz and continued to Krakow, Budapest, Vienna and return to Prague and ( by night train to) Amsterdam . Two of the 4 in the family opted to return to see Birkenau, but the other 2 explored Krakow. Car is easy especially for 4 of you, roads were good tho there was construction. Take a GPS or have a data plan on your phone.

I figured you looked at a map before you asked the question. So here is my answer, if I absolutely had to go to three places totally removed from each other in 10 days.

Fly into either Zagreb or Ljubljana; which ever works best for the whole plan.

Then you can fly to Krakow for about $200 with one stop (usually in Warsaw) in under 4 hours.

Then Krakow to Prague on the night train.

Then home out of Prague.

There are probably 4 other less than ideal routes.

As others said- the destinations are quite apart for 10 days. I would adjust them Slovenia and Croatia and drop the rest. Or Prague, Auschwitz, Krakow and Slovakia instead of Slovenia.
Prague to Krakow about 7 hours by train direct. About 5 and half hours to Auschwitz by direct train from Prague.