If you're doing MUC on the outbound I'd do FRA on the return. Enough to burn 2 days around FRA and enjoy it. I don't hate FRA airport as much as many on these boards but take that with a grain of salt.

What you haven't said is if you come back through FRA do you shorten your trip in BER? If so I wouldn't do that. BER is, by far, the most interested of the three cities IMO. If you aren't shortening your stay in BER and can still do FRA go for it. Otherwise take the longer layover on the return from Berlin and, yes, you can nap in the UA Club. Just good luck finding a quiet area to do that.

-RM