Please check out http://www.merrillhouse.com
and for reviews from other families and an availability calendar see http://www.vacationhomerentals.com/34720
It's a family friendly place that sleeps 20+ (thinking you might want to bring family in addition to your brother, nephew and you) in the summer with good (walk-in) access to the Rapid (both Middle- and Lower-Dam) as well as the region in general, from the Magalloway and Upper Dam to Kennebago to Rangeley, boating on the Richardson lakes, kayaking and fishing the Androscoggin River, both in ME and in NH, and lots of little waters in between. It's located in Andover, a really nice, small old-New England town, and reasonably close to Bethel too, if you want to take in some of their attractions.
I've fished pretty much the whole region in every season (except when I'd rather be skiing), and can assure you the fishing is fine in the summer!
I'm biased as it's a family business, but it is truly one of the best locations for accessing the Western Maine mountains region, and is one of the best family vacation spots I know.
Thanks for asking (and giving me this opportunity to submit this plug)!