The OP is traveling with his family and transfering to an ICE train (presumably). The S-Bahn line at SXF only feeds into the Ringbahn. It doesn't feed into the main east-west line, and hasn't done so in a couple of years (ever since DB started reconstructing the Ostkreuz station). From my recollection the SXF S-Bahn ends up at Pankow station (feeding into the eastern section of the Ringbahn). And IIRC, there is a S-Bahn line during morning and afternoon rush hours that goes to the Südkreuz station. That means he would have to transfer trains if he took the S-Bahn. IIRC, the ICE trains to Hannover start at the Ostbahnhof station and stop at the Hauptbahnhof and Spandau stations. Which is where the Regional Bahn trains go directly from SXF.

And to the OP, if your train to Hannover starts at the Ostbahnhof station, and you plan on taking a taxi instead from the airport, it will be less expensive to take a taxi there (and quicker) than going to the Hauptbahnhof. Plus, the Ostbahnhof station is much easier to navigate than the Hauptbahnhof.