It's not difficult to learn a new language, especially if you're surrounded by it. Might take a few months or so before they're semi-fluent enough to get around, but guaranteed it'll pick up fast from there. My sister's been in Germany for ~1.5 months, definitely has been the case for her.
I'd say the same thing as I said last time: go over a month early yourself, leave the family to start brushing up on their german and get things sorted at home, while you get things ready over there.
Germany is a nice place to live, and the distance from so many other cultural areas is great too. A 1hr $70 flight can get you into any number of other countries, I'd definitely want that for my kid. Travelling really opens your eyes in a way that not much else can.