Most exploring will have to be in your free time and on your own. Public transportation in and between major cities is great, in the countryside or between small towns and villages its poor. It s not fair to expect your relatives to expertly tour guide you around, they are not professionals. People are always least knowledgeable about their local area and the same go s for over there. Group tours vary greatly, with some stopping only at the most known tourist sites, while others take people off the beaten path - make sure you check and understand the tour itinerary.
Most tours do the standard cookie-cutter itinerary to the same places.
If your interested in seeing and learning how items are created or learning more about the historical significance of folk art items from the artists, folk dance groups, etc, they are very difficult to find on your own. A licensed local guide will know many more fascinating details about, local history, stories and legends than are to be found in any guide book. To really understand the people and background of these countries means you must learn about their history. The best person to teach you, is someone who has lived through it, and has a genuine love of history and the importain role that the Czech and Slovak people played in it. While some guides and researchers do their work because they love it, others are more interested in the amount of money they can make from you.