I don't know which country's Hertz T&C you quote from - it differs from country to country, especially given that Hertz does have a large footprint in many of the countries on the "no go list", including HR and HU. When I rented from Hertz HU, I definitely have no issues driving to HR, SK, SL, etc. Same for rentals in AT. Just inform the counter which countries you plan to drive to and they might slap a small extra charge on the rate and include in your rental agreement - this latter is important for insurance purposes.

Given that you'll be with family and wanting to plan ahead and play safe, the best advice would be as someone said upthread to contact the local Hertz (etc) office and ask a quote while mentioning the countries you plan to visit.