A Sachsen-Ticket will get you to the Czech border. The Sachsen-Böhmen-Ticket will get you into a part of the Czech Republic (see map, page 4. Ticket is valid for blue lines in the CR), but not all the way to Prague, only to Litomerice. However, at that point you will be in the Czech Republic, and you should be able to purchase your tickets for the rest of the trip from the conductor (not sure if he takes Euro). Czech Rail shows the fare from Litomerice as about €4,43 (113 Kc). For all four of you that would be 4 x 4.43 + 32 = 49.72 EUR. The trip takes a little over 5 hours. The Sachsen-Böhmen ticket is always available at the price, €32, from any automat at the Bahnhof in Dresden.
Alternatively, if you purchase ahead, you can probably get Europa-Spezial Tschechien tickets for €19 pP, €76 for all four of you. Those tickets are date and train specific, and non-refundable, so you lose some flexibility, but you can travel in a much nicer, Eurocity train all the way to Praque in just over 2 hours.