Family wanting to explore Rhine Valley

St. Goar is a good central location. Bacharach and Boppard are 10 minutes away and good towns to explore on the same side. Oberwesel, another nice village, is only 5. From St. Goar a ferry there takes you across to St. Goarshausen where you can catch a train to destinations on the other side of the river - Braubach (Marksburg Castle) and Rüdesheim for starters. Rheinfels castle is right in town.

Rheinfels Castle
Marksburg Castle

Local tourist info office websites will list apartments that you won't find on most other sites.
I've used the Loreley apartments previously. 4 of us stayed in the Rheinblick (Rhineview) unit. There are 3 other apartments in the same building. Close to everything, nice place, great view, very nice owner.

Loreley-apartments

Other apartment listings in St. Goar HERE

Boppard is 10 minutes north of St. Goar by train and a good base town too especially if you wish to visit the Mosel River on day trips.
Boppard tea house
Boppard waterfront
Boppard TI listings

I suggest looking up Bavaria Ben on Google. He has a great tutorial on the Rhine River Valley.

His views of the B&B's and restaurants in Bacharach are right on the money.

Mixing 3 generations of travelers is tough, especially when 3 are so young. And traveling with 7 people is also difficult logistically. It's almost as cheap to travel by a full size van, but such a rental is quite expensive.

I would suggest you find one central location close to a train and do day trips out of there.

Several of Rick's hotel listings for Bacharach on the Rhine (and elsewhere) do have quad rooms, but then you have to confirm the actual bed configuration when booking. Many "double beds" are made from two singles that can be pulled apart. For instance, send email to pension.lettie@t-online.de or to winzerhaus@gmx.de, each of which should have quad rooms for about €95/night. These places don't have much in the way of web sites.

Also consider the Youth hostel in Bacharach, in a hilltop castle, which has rooms with 6 - 10 beds. Taxi from the train station costs €10 (x 2 = €20 for your group).

Atmospheric though the castle-hostel in Bacharach may be, it's about 500 vertical steps up a hillside from town and nowhere near the station, the dock, cafes, or restaurants. The location discourages even fit folks from coming and going on a whim.

As for accommodations your needs are pretty unique. You can consult other sources of course like Rick Steves and Bavaria Ben's Bauernhof, both great resources overall, but their focus is on smaller groups and tend less toward the self-catering options you mention. If you need help, the pros are the ones in the local tourist offices who really know their towns (and probably everyone in them.) Here is the contact info:
Rhine River TI Offices

I love Bacharach (after three visits) but it is too small to be a good base for day trips, unless you really lilt that. St Goar would be my choice too.

We stayed at the Winzerhaus this past Sept. I think it is a great place for your group but you should book early. It's a smaller, clean place that's budget friendly. Cute Bacharach town. Walking distance easily of ferry and train to explore the Rhine. Check out the Tripadvisor.com reviews.

We found St. Goar a good location for exploring the Rhine by train and rented an apartment for a week here: http://www.hotel-zur-loreley.de/st-goar-germany/index.htm It was two minutes on foot to the train station.
Ours was a three-bedroom, two bath for the two of us! You could get a couple apartments, as the landlord has some on the floor below. Note: no elevator, no air conditioning in case you hit a heat wave in summer. Not sure about the single beds; I think ours was two singles pushed together, but didn't study the unused bedrooms.

Take a look at Eltville. It is only a few minutes by train from Rüdesheim and in the summer, at least one ship a day stops here. Lovely little town, absolutely charming. Well known for its' roses and wine. Google it for photos. Eberbach monastary (where they filmed the Name of the Rose) is a 15 min. bus ride away, lots of wine bars, a wonderful promenade along the river without a road or train track blocking the view. Old churches, dry castle moat, tower keep, vineyards and a regular train at least once an hour in both directions. Kiedrich is near by town to Eltville (the bus to Eberbach stops here) with a church dedicated to St. Valentine and with the oldest organ in Germany.

A very special thank you to all the people who took the time to respond to my questions. You are a wonderful community out there. It is refreshing to see so many people helping others when perhaps you don't need to be using your precious time this way. I am working through your responses and getting your ideas sorted for our lot!
Thank you again
M