I'm thinking of traveling from Amsterdam through the Rhine/Mosel area in late June, spending 5 days from Bacharach to Baden Baden, before heading to Paris/Normandy. (I have a friend in Amsterdam and in Heidelberg).
WRT the Rhine/Mosel portion, I am not a big wine-country person, but love the outdoors and historical architecture and art.
Here's my current idea: Train from Utrecht to Koblenz in the afternoon (4 hrs), renting a car there (for the rest of the week, which I drop off before leaving Baden Baden) and driving to Bacharach for the evening/night. Next day (aka Day 1) spent between Bingen and St. Goar (maybe doing the cruise, maybe just driving around doing things). Another night in Bacharach. Next morning (Day 2) drive to Beilstein on Mosel (approx. 90 min), sightseeing for the day, maybe renting bikes and/or hiking. Spend the night in BoM. Second day (aka Day 3) along the Mosel, do more there, or drive to Trier for the day if we are feeling done with quaint river villages/castles. Sleep again in BoM. (Day 4) drive to Heidelberg (almost 2 hrs), visit friend. Sleep in H or in Baden Baden. Day 5 rest day/easy day in Baden Baden and return car. Day 6 Train to Paris.
Q's:
1. I'm leaning toward a rental car bc of ease of meandering in this area and without being married to train schedules, less time spent on transport - waiting for trains/switching trains - and ease of storing/retrieving my stuff. Is this foolish? Would the trains be just as easy, facilitate as much ease of exploring, etc. What would you recommend?
2. If we (13yo daughter, me) had a car, do we still want to do the cruise from Bingen to St. Goar. Coudnt we see a lot of the same things from the road, walking around the towns along the side of the river?
3. Anything you particularly suggest? Particular hikes? Is Trier not worth the time (I love the idea of the ruins, but not of squeezing in more). I'm figuring every day has a half day spent with a to do list, and the second half open ...
Having spent time in Koblenz and a day in Trier, I would say that Koblenz is the more obvious tourism day, but Trier is actually the more attractive town. The both pale beside Cologne (bigger city). I haven't been to Baden, but I doubt that it is one of the nicer places (today) in the BF. Freiburg is sort of a mini-Trier, with no Roman remains, but I liked it.
It's a matter of taste whether you take the KD boat ride (one way, downstream!) from Bingen to Boppard (or Bacharach). But most people agree that the view and the leisure strongly favor the boat. If you already have the car, you should park it for that day and take a cheap, fast (10 times faster than the boat) train to Bingen, so you don't have the millstone of the car tied around your neck. That's what we did from Koblenz.
Otherwise there's nothing wrong with your list, but there are a vast number of just as good alternate stops. For example, while people think of Traben-Trarbach (T-T) as wine country, the town actually has a nice bit of soft (my preference) hiking and biking. If you see a Rhine castle inside, you don't need to see (unmentioned in the OP) Burg Eltz. I believe the BF is unmatched for hiking-many trails have three degrees of difficulty to choose from between some towns. You want to stay in a place that gives you the KONUS card so (like that pesky, non-California plan I gave you for the boat) you can train for FREE to the trailhead and walk back to your hotel-which you have chosen for access to nice walks.
I can't emphasize enough the importance of research, beyond what you can get on a newsboard. For example, we ran across the Jugenstilhotel Belvue in T-T. I think you might want to stay there. Likewise, it's not architectural OLD history, but you are in danger of completely missing the Vitra Design Museum and (interior design) showroom in Weil am Rhine, where the longer architecture tour (including Zaha Hadid's first completed building) always books up in advance. Not far away (make sure you can drive the car in Switzerland) is the nice, quiet Roman site of Augusta Raurica. (Note that my ideas relate to the southern BF, and you wanted to go north.)
Trust you know that Normandy is a good bit beyond Paris.
You've asked a ton of questions. I'll try to respond just to the car/train issue for now.
BoM? If that means Beilstein you'll probably need a car. Beilstein has become a Rick Steves cult favorite, but having been there, I don't quite get it. It's the length of a few tour buses long and there's little to do there that can't be done in a couple of hours.
https://upload.wikimedia.org/wikipedia/commons/7/73/Beilstein_%28Mosel%29,_2012-08_CN-01.jpg
I prefer a town with more to see and do. Staying in Cochem (my first pick) or Bullay or Treis-Karden or Winningen (if you want smaller towns than 6,000-population Cochem) would IMHO eliminate the need for a car. Train service is very good between Koblenz and Traben-Trarbach along the river - there are 17+ trains per day in each direction between 6 am and midnight along this route. On the Koblenz-Cochem-Trier route there are 30+ trains per day in each direction. Trains are frequent and dependable along the entire Rhine as well, where they run on both sides of the river.
Also, you'll be needing to use the trains anyway if you do a cruise (to reach Bingen and to return from St. Goar to Bacharach.) I recommend the 1.5 hour Bingen-St. Goar cruise as the best way to enjoy the scenery. Driving just isn't the same.
If you were in the Rhine/Mosel region for 10+ days then maybe a car would be good for greater exploring but the towns with stations on both rivers will keep you plenty busy since you have just 3 days.
The trip to Heidelberg is simple by train as well.
There are day passes for trains around the Rhine/Mosel - a VRM "mini-group" day pass at €22/day, and the Rheinland-Pfalz ticket (€29/2) which covers a broader area. No gas, no parking fees, no traffic, easy hop-off, hop-on usage; you get a 20% KD cruise discount with a valid train ticket as well, and the ferry crossing in St. Goar is free.
http://www.vrminfo.de/en/tickets-and-fares/ticket-offers/leisure-ticket/