You've gotten some good advice below. I'm just going to go through your entire itinerary and post my thoughts in italic. Certainly you don't have to change anything because of this, but there are some potential problems in here as everyone has noted.
Day 1 - after overnight arrival - Marienplatz, Hofbrauhaus, English Garden. Overnight Munich (this is fine)
Day 2 - Neuschwanstein castle (tour including transportation). Overnight Munich
(I wouldn't visit Neuschwanstein Castle but if you want to go, you should. This is fine too.)
Day 3 - Day Trip to Rothenburg ob der Tauber & Nurenberg (private driver). Overnight Munich
(This is where it starts to get in a little dicey. Taking a day trip to Rothenburg and Nuremberg is making things so tight that you will not get anything out of it. I would skip one or the other.)
Day 4 - Dachau (on our own via train)/BMW Tour. Overnight Munich
(Again I think doing both Dachau and BMW in one day is problematic, although it it is definitely more doable than doing Rothenburg and Nurenberg in one day. That said, when you are done with Dachau, it will affect you, so you may not feel like doing a BMW tour.)
Day 5 - Zugspitze (tour including transportation). Overnight Munich
(This is fine).
Day 6 - Day trip to Salzburg via train. Overnight Munich.
(This is fine but if it were me, I would spend the night in Salzburg. You're not really going to get anything out of going back to Munich although I guess it would save you changing hotels. That's really the only benefit and Salzburg is so gorgeous and lovely that I would take every minute of time that I could squeeze in there. You'll have the whole day and evening in Salzburg and the next morning you can relax and get on a train and head on your way to your next destination.)
Day 7 - Train to Cologne. Drop bags at hotel? Visit cathedral
(At this point, it gets really problematic. If you want to see Cologne then go to Cologne and spend days 7 and 8 there. Then head down to Frankfurt and fly home. If you want to see the Rhine, then skip Cologne and head to some place like Boppard, which is a good base for that area, visit the castles and take a cruise along the Rhine. Stay there for two days and then head back to Frankfurt and fly home. But I wouldn't try to do both. You'll just exhaust yourselves. My vote would be for the Rhine. I do like Cologne and I love the cathedral but the Rhine will give you a chance to relax and enjoy the beautiful scenery, the river, the gorgeous castles and and all the ruins along the Rhine).
Day 8 - Day Trip on the Rhine - st goar to bacharach and marksburg castle visit? Have been confused in reading about this idea so not sure if this is wise.
(See note above. FYI, when I was there I stayed in Boppard and took the train down to Bingen to the south, then got the KD Ferry in Bingen and took it back all the way back up to Boppard. I saw so many ruins along the way, I agree that limiting the Rhine cruise between St. Goar and Bacharach will cause you to miss a lot of the sites. Definitely go down as far as Bingen or even Bacharach.).
Day 9 - Fly home
Anyway, those are my thoughts. Use them or not. It's your trip so you should do what you want. No matter what happens, you'll be in Germany and it's a wonderful country so I'm sure you will have an incredible time.