You will be fine, I went down last weekend with full camping gear, coolers, and even fire wood and only got stuck once because I changed my mind of where I wanted to go and got stuck. I was going to say colorado river center, but I think it looks like you found that. If you are interested in camping, send me an e-mail to dave(at-sign)davedempsey.net and I'll send you a PFD document of the BLM guide that has the camp sites marked on the map. Er, I mean PDF file.
There isn't too much white water, lots of flat water, a few small rapids, one that you may have to row a little bit for, but not much. It is a fun "booze cruise" camping/fishing/floating run if you aren't going with the intention of running much interesting whitewater. Also, your shoulder muscles will be ripped by the end of the trip if you row the afternoon flatwater headwinds! Might be worth renting a ducky or something to keep things interesting for your parents.
P.S. Be aware that anywhere you camp with have train traffic at night, so if you have any light sleepers who will be grumpy....