A rental car is an expensive nuisance in Munich. Believe me when I tell you, parking is very hard to find within the inner ring. Only the most expensive hotels can guarantee a spot. Most German cities are relatively easy to navigate by car, but Munich is one of the more prominent exceptions, even with a GPS. Don't bother with the car until you leave Munich, and even then, it isn't really necessary for what you have suggested... sort of...
As the others noted, the Black Forest is a vast region, not a single destination, and it isn't that close to Munich. You pretty much have to drive either through back roads, or through Stuttgart to get there, both of which options are very slow. Plus...despite the attractive name that translates nicely into English, it isn't all that much different from any of the other 50 or so forested mountain ranges that criss-cross southern and central Germany. If you want to hike, rather than go far out of your way to the Black Forest, just head an hour south of Munich to the much higher and more impressive Alps. You can combine your hiking outing with a visit to Neuschwanstein. But keep a little flexibility in your schedule. You can never count on the Alpine weather gods to grant you with favorable conditions, especially if you pick a day far in advanced without the benefit of a short-term weather forecast. And the one caveat I'll offer is that hiking in the high Alps usually isn't possible in early May, but some of the lower slopes should give you some good options.
Rothenburg odT really isn't unique enough to justify going that far out of your way to visit, and certainly not for two nights. See it if you must. But if you have to drive more than an hour or two out of your way in Germany to see Rothenburg, you've probably passed several far less touristy alternatives.
Finally... if you're flying into Munich, I can't imagine a better place to spend part of your honeymoon than Therme Erding, located about a 15 minute drive away from the airport.
