"Are 4 nights in Bacharach too many? Yes, planning on one day exploring the Rhine via boat to St. Goar as RS recommends. One day to relax and enjoy Bacharach and 1 extra day for ????? What do people think of Rothenberg after Bacharach or before?"
I would absolutely NOT race off to distant and uber-touristed Rothenburg when there are so many things to see and do in Bacharach's back yard, some of which RS mentions in his book, and other things that I believe RS has probably overlooked on his trips to the area.
Oberwesel (5 minutes from Bacharach)
Wander Oberwesel's old town wall and towers
Excellent Open air museum in nearby Bad Sobernheim
Rheinfels Castle (castle ruins, St. Goar)
Marksburg Castle (in Braubach, an intact, never-destroyed castle with period furnishings - good tour.)
Chairlift ride to Gedeonseck cafe overlooking Boppard
Linz am Rhein, maybe the Rhine's most attractive village of all
If you want some place a bit extra-touristy but still fun, try Rüdesheim, across the Rhine and south of Bacharach (use ferry in Bingen.)
And there's more in this region - see this guide.