"...7-8 days drive/train/fly around from Frankfurt all over the south side of Germany. After which we are left with 4 days..."
Frankfurt - Kröv: We had planned to travel from LUX to Kröv last week but instead had to make an unplanned train trip to Kröv from FRA airport (thanks for nothing, Ryanair for cancelling my flight to LUX.) Anyway, it's a fairly easy (and extremely scenic!) train trip though you'll have some changes of train in Koblenz and Bullay at a minimum. The final segment (Traben-Trarbach train station to Kröv) is a very short trip normally done by bus. In our case we couldn't leave FRA before about 16:30 because of the flight switch, so we finally got to T-T just before 20:00 - and grabbed a taxi to Kröv (last bus leaves Traben-Trarbach at around 19:00.)
Now, you could perhaps rent a car and drive from FRA to Kröv, but I would not. An overnight international flight across several time zones could lead to impaired driving.
Tickets: at FRA Regionalbahnhof station, we bought two €5 VRM tickets to Mainz (€10) plus one Rheinland-Pfalz ticket for two (€29) to cover the whole trip to Kröv. If you get the same tickets, the 3 of you will pay €15 + €34. The R-P ticket is a day pass that covers regional trains AND buses and is valid after 9 am - so as long as your train leaves (or passes through Mainz) after 9 am, this ticket strategy should work for you as well. There are ticket machines at the station location and at the platforms down the escalator from the station. The machines may be finicky about what bills you use - so have a nice variety of them handy.
Kröv, Traben-Trarbach, and Bullay all have their individual charms, from hiking and biking to wineries, etc. But the closest tourist gem in the area is Bernkastel. Be sure to take them there. We caught a 10:20 am river cruise out of Kröv to Bernkastel for a really nice and scenic float (about 1.5 hours) and I cannot imagine a bus ride being its equal.
In our case we did not return to Kröv but took our bags with us and after a few hours there caught the bus to Wittlich to rejoin the Mosel River train line (bus 300 leaves from the "Kues Forum" stop behind the old train station there.)
As for your other days in Germany... You'd be wise to consider a prolonged stay in the immediate area. Trier, The Rhine Valley (medieval castles like Burg Eltz and Marksburg, river cruises, old-world villages) and cities like Mainz, Speyer or Cologne really deserve the time and are somewhat smaller and easier to navigate on foot - and they would greatly reduce the ground travel time and expense you will otherwise have. You can fly (if you want to) to Munich or Berlin afterward from FRA, Frankfurt Hahn, or Cologne, perhaps, but I would take the train instead - a lot less hassle altogether IMO.