Car rental or train- lower cost for family of 5?

You can get fuel usage estimates by inputting the route at www.viamichelin.com You can google current fuel prices in Germany and fuel mileage, er kilometerage, for the model of car you want to rent.

Looks like trip has 3 phases.
Munich, don't need and should not want a car.
Munich to Frankfurt area, rent a car to visit the various places on the way.
Rhine area, don't need a car, but maybe useful for a few things. It will set a lot, but could be handy getting to the airport. Trains may work just as well. For instance, it is 34.50 EUR for a group ticket from Bacharach to Frankfurt Airport Regional train station for the whole gang.

eventually a night train down to Rome departing from either Frankfurt or Munich.

The only night trains from Germany to Italy depart from Munich, there are no night trains from Frankfurt.
Website for the company running the trains: https://www.nightjet.com/en/reiseziele/italien.html
Independent review site: https://www.seat61.com/trains-and-routes/nightjet.htm

Three grown-ups, one pretty close and a near-teenager accustomed to squeezing into the middle seat -- plus luggage -- will need a vehicle that's larger than the standard European rental. Shop carefully. And speaking of "standard", there are plenty of stick-shifts on rental agency lists so take that into consideration too.

"We will be spending about 8-9 days in Germany next summer."

2019, right? Ground travel only, right? I'm assuming you don't have flights bought yet. I'll suggest that you fly into FRANKFURT instead. Head straight to the nearby Rhine first - at least 2 nights there - then to Rothenburg and Munich afterward, and to Rome after that via Bologna. That way you're traveling only southbound - no long northbound journey at the beginning.

I don't necessarily recommend visiting Rome in summer. But if you're going there, you'd be wise to look into cheap flights before jumping on the night train idea.

There's usually no need for a car once you're on the Rhine. Trains cover both river banks in each direction every hour and connect all the towns. The Rheinland-Pfalz ticket will cover all of you for €39/day. You might use the VRM mini-group ticket - only €20 - to get around instead if your destinations are within the VRM zone.

Rhine to Rothenburg trip: There are a number of ticketing strategies possible depending on the day of the week. If you can schedule this trip on a Saturday or a Sunday, the Happy Weekend ticket will get you there. It works out to about €15 each.

To Munich: one Bayern Ticket will do it.

Thank you so much for the fuel estimate web site and info. on trains etc. We are actually going this summer 2018 and we got flights using award travel so flying out of Venice was one of the only scenarios that worked. Already booked our short flight from London Luton into Munich because of a great price and wanting to take our teens to Dachau. Also meeting up with friends in Rothenburg area on certain days so some of the order of our trip dictated by that instead of logical geography. Your helpful links will allow me to crunch some numbers to decide when to get a car as we zig zag around the area.

We backpacked for 6 weeks when first married 20+ years ago and did lots of night trains so we thought the Frankfurt/Munich to Rome would be a neat experience to share with our kids. It's not cheap though! Seems about the same cost as a flight except that we would also be saving on NOT having to pay lodging for that night and not sucking up part of the hours of daytime doing the airport check-in and flight. I was thinking we might be bringing back car to Frankfurt, taking a train to Munich and then getting on the Night train there to Rome. Can anyone advise on Nightjet for this route and what to expect? We know it can be hard to get a good night's sleep on the train... any advice for smooth and fun journey?

www.seat61.com for information about train experience through Europe (and the world). Use the search box for description of the Rome Nightjet.