Use www.bahn.com to investigate train schedules.
You'll see there are direct trains (no changes) between Frankfurt airport and Bacharach every 2 hours. You can use connections at other times if you wish. Deutsche Bahn does not actually sell this ticket because it is in the Rhein-Main district (the RMV), but you can get the 11.60 per person tickets from a vending machine, or at a ticket window for a 2 euro service fee.
Spend a little time on the website for an explanation of how "Laender" tickets and "Quer-durch-Lands ticket work. http://www.bahn.com/i/view/USA/en/prices/germany/regional-offers-overview.shtml
You will need to change trains at least 3 times to get to Rothenburg, at Frankfurt, Wuerzburg, and Steinach. If you take all local trains, (almost as fast as the ICE trains because the distances are short), the cost is 44 euro for the first person and 8 euro for the second person. You must leave after 9 am weekdays, but you can take any local train and stop off on the way if you wish. On weekends you are not restricted to the 9 am start time and the pricing is slightly better.
Rothenburg to Munich is all in the state (Land) of Bavaria, so there they have a ticket called a Bayern Ticket. It works similarly, just restricted to Bavaria, but costs less.
There are several direct trains every day between Munich and Zurich. There are also busses operated by Deutsche Bahn that are actually a little faster. These are International trains and busses, so just buy a ticket at the station if you are not in the mood for finding deals on the DB website.