I used Gengenbach as a base and really liked it. I think you'll find it a nice change of pace from Amsterdam and Paris. It's a small, quiet town with a great central square (more of a triangle, actually) across the street from an Italian restaurant that has a gelato window. My friend and I ended all of our days there relaxing on the square, eating gelato and people watching. There is a Wednesday morning farmer's market on the square. There is a hike that can be done through wine fields up to a chapel that sits above the town.
As for Gutach, the open air museum (Schwarzwälder Freilichtmuseum Vogtsbauernhof) is great and has a train stop directly in front of it. Next to the museum is a summer toboggan run (Sommerrodelbahn Gutach) that your family would probably enjoy (here is a YouTube video by a German kid on the Sommerrodelbahn). You could combine a visit here with a visit to Schiltach to see the attractive town and the reconstructed water-driven timber saw at the Schüttesägemuseum. There is a nearby zipline course, but, unfortunately, the minimum age is 12.
Other options in the area:
1. Baden-Baden if you want to hit the spas or the casino -- you can be like Rick and drop the kids off at a pool.
2. Go to Freiburg, a college town in the south with a variety of sites to see and with good hiking around it
3. Go to Triberg -- not for the touristy town, but for hiking. The train ride there is nice. The town itself is terribly, terribly touristy -- it's the cuckoo clock capital of the Black Forest. I like going here for a nice hiking trail (the Schwarzwaldbahn Erlebnispfad) that starts at the train station, which is at the opposite end of town from the touristy part. The trail takes you through the forest to sites related to the Black Forest Railway (Schwarzwaldbahn) -- and (sigh) past the world's largest cuckoo clock. The path has 2 loops -- I would just take the first one (stations 1-8 on this map), which is the more forested part of the trail. It's 6.5 km and takes 2 hours without stops. We did it in more like 3 1/2 hours because we waited for trains at some of the stations (not train stations -- but info board stations) and waited for the world's largest cuckoo clock to cuckoo (disappointing). It's not a bad hike except for a pretty steep ascent on switchbacks after the world's largest cuckoo clock and a fairly steep descent back into town. If you do it, take plenty of water. At the other end of town are the cuckoo clock stores and Triberg Waterfall, which I kind of enjoyed but I like tumbling water.
4. If the kids are tired of old European buildings, find out how Germans do theme parks at Europa Park at Rust.
5. Normally I would recommend a trip to Titisee and Schluchsee -- a short stop at the former to see the hoards of international tourists (and commercialism at its worst) and a long stop at the latter to hang out with vacationing Germans (hiking, biking, swimming, boating). The train to the two lakes take you deep into the forest, but, sadly, the trains are not operating this summer due to work on the train line. So, the trip is by bus, which I'm not sure would be the same (and seems to be more time consuming).
Russ will probably come along and make other suggestions.