Rio Chama is a beautiful little western river.
Top is forested with plenty of really nice camp sites.
Bring your drinking water.
The issue is water releases so check with BLM offices in Taos.
If you are in a say 14 ft self bailing raft with experience, should be ok at normal flow. I recommend a self bailer raft so the kids can have a place to set so they can hold on and reasonably safe from getting thrown out.
Rapids are for the most part pretty straight forward. There are at least three or four that require heads up good rowing skills with kiddos on board. Couple of really tight bends where the current pushes you into the wall and others pretty much wave trains with plenty of bounce for kids in a raft. Worth a scout run before taking the kiddos I think.
Since you mentioned 2015, would be great if you ran the Rio Chama with adults just to get the hang of the drops to scout and camp sites. Highly recommend you do a scouting run before taking the kids.
Over all this is one of my favorite rivers to introduce folks to multi day river trips.
Permits some times hard to get but you can do the full day run (most of the major rapids are there) by putting in just below the Monastery and all you have to do is sign up. Beautiful scenery on the way down and back from CO by the way.