Ok... Here's what looks reasonable to me. I've changed the order of things a bit. (You do not want to step off a plane and ride regional trains all the way to Stuttgart...)
Nov. 29 and 30 would be excluded from the D-Ticket since it is a calendar-month pass. See ticket suggestions below for those days. No pre-purchase is necessary - just buy them on the day of travel.
1/29: FRA > MAINZ by direct regional train for 2 nights... use a "RMV group day ticket" to get all 5 of you to Mainz for €22. Mainz is almost as close to FRA airport as Frankfurt is. Travel to either the Mainz Hbf station (the main station) in 25 minutes or to the Mainz Römisches Theater station in 20 minutes. I like the Römisches Theater station because it's closer to the nicest part of Mainz where the Dom (cathedral), Market Square, the old-town zone, the riverfront walk, and the Stadtpark (city park) is. However, there are more hotels near the main stationn. There's an IBIS hotel right near the RT station, and the Hof Ehrenfels hotel is right in the old-town section. A few other hotels are near there as well.
1/30: Day outing down the Rhine by train ... A Rheinland-Pfalz Ticket for 5 persons (day pass) (€65) will cover your round trip to the river towns and back to Mainz. Hop on and off at will anywhere you wish. There is a DIRECT regional train from Mainz MRT at 9:45 (or Mainz Hbf at 9:51) to Koblenz (takes one hour) or to any other towns you wish to stop in on the way (Bacharach and Boppard make sense to me.) The same day pass gets you from Koblenz to Braubach (for Marksburg Castle) on the east bank railway, which you can use south to Rüdesheim, Wiesbaden, and for the final return leg to Mainz, all on the same ticket.
Rhine Valley transport map north of Mainz: http://www.loreley-info.com/eng/rhein-rhine/walking-hiking.php
Other trains in the morning will get you north at different times as well (but most leaving from the MRT station require a change of train at Mainz Hbf.
12/1: Mainz > Heidelberg Hbf or Heidelberg-Altstadt, about 1.75-2 hours by regional train (D-Ticket) w/ 1 transfer either in Mannheim or in Darmstadt, depending on what time you depart. I like the 8:52 - 10:39 journey where you change in Darmstadt Hbf (which I do NOT know well - but maybe stopping there on the way to H'berg, as our colleague Bigtyke has suggested, would be enjoyable. Use the Darmstadt Hbf station lockers for your bags while you sightsee. 12/2&3: possible day trips with the D-Ticket.
12/4: Heidelberg > Stuttgart Hbf, about 1.75 - 2 hours by regional train (D-Ticket) with one change of train 12/4,5,6: possible day trips with the D-Ticket.
12/6, afternoon: Pick up your bags from the front desk at your Stuttgart hotel and catch the regional train (D-Ticket) back to either FRA airport or to MAINZ. This is a longer journey by regional train - the 14:59 departure stops in Karlsruhe (change there) then in Mainz Hbf (17:47, change there for FRA) with final arrival at FRA at 18:28. MY PREFERENCE would definitely be to end the trip in Mainz for a nice dinner and final night... then in the morning head to FRA on one of the many direct trains to the terminal. (There are later departures for Stuttgart > Mainz > (FRA) as well, but finishing up the travel by 18:00 would be my choice.)
Alternatively, you can spring for faster ICE train tickets from Stuttgart to Mainz or to FRA airport. How much faster depends on when you depart Stuttgart. However, most of the saver fares for 12/6 are currently running over €100 each with a couple at €75 each or so, which is a lot compared with "free." Direct trains from Stuttgart to FRA the next morning are in the same price range right now. Price aside, I would still want to be closer to FRA than Stuttgart (or Heidelberg) on the morning of my flight home, just in case some railway problem came up and I had to take a taxi (which could be done from Mainz.)