I am hoping that someone out there has experience with a layover in Germany with Lufthansa and can give me the probability of Lufthansa extending my (less than) 24-hour layover to the next day without cost or a creative way to earn 30K MileagePlus miles outside of the Chase United Credit Card.

First, I used 60K United Mileage Plus miles for 2 passengers on a flight returning from London back to Washington DC in May.
Second, I noticed that I could fly from London with Lufthansa to Berlin, stay over about 20 hours and then hop back on a Lufthansa flight back through Frankfort and home to Washington DC.
Third, I am flying with my 21 year old daughter and would like to show her more of Berlin so we want to stay an extra day.
Finally, MileagePlus requires 30K more miles in my wife's account (from which I purchased the flights) to make that change. We already got the Chase United 50K bonus and have zero now. I don't see any way to get the extra 30K needed for the flight in time.
I may have 40K in my MileagePlus account by May, but I checked, and the United website requires I get the miles from my wife's account. (gifting them is almost as much as buying a cheap flight!)
Any thoughts/advise from experienced FlyerTalk folks would be appreciated.