In an effort to raise a child with exposure to anything other than just English like many US kids until high school, (which I think puts them at a HUGE disadvantage). I did a little research on the matter last year. The book I liked the most for readability and its seeming ability to support its own theses with corroborative evidence was "The Bi-lingual Edge."
In this book, they suggest that it is common for kids raised to speak a "family language" in the home while hearing and using another popular language outside of the home to stop using the "family language" shortly after entering school. The result (here in the states) with many of these families is a child that grows into an adult that understands a second language fluently, but can't recall vocabulary and sentence structure well enough to effectively communicate in that second language once their parents are no longer around and using the second language.
The suggestion the book's authors make, is to refuse to "understand" or "respond" to the language popularly used in your area in regard to use with your child. While I understand that you are clarifying they already know that you can use German, it is possible to use this tact anyway. I have always used it even within English alone if I don't like the tone used.
"But Mo-om. I don' Wan'na clean my rooo-ooom!"
"Oh I'm sorry I don't understand Whine. Could you say that in English (or on "German Days" German) please?"
For you, It might be more like, (In Danish) "I Choose not to respond to German. Could you try again in Danish Please?"
Your child may sometimes choose not to try again. This may mean he solves the problem for himself, or goes and seeks out Mom. However, if you start from a very early age (where you are at now and what you are already doing) a lot of times, just trying again in Danish will be easier and that is the choice your child will most likely make, most of the time.
When, sometime your child complains about it, you can simply explain that it is to their advantage to know as many languages as possible and to retain and maintain their language skills they have to regularly use the language. If they know that is your stand and know you will not repsond to the use of German, but will only respond to the use of Danish, they may get that adolescent annoyance with you at points in life, but you are the parent and are doing what you believe is right, and enforcing what you value. Of course, in mixed company, you should all be able to use the language best suited to the situation, (Use German with their German friends rather than awkward, forced translation . . .) but in regard to the day-to-day that is what I've seen as the supported hypothesis for best handling the situation.
I'll admit, I'm still testing the waters with my own and far from fluent myself, so my experience is pretty thin. At the same time, I've seen so many friends and family members lose active speech for lack of practice (myself included) and think it is a tragedy to toss away such a gift lightly. Parents don't like to admit to "forcing" kids to do things, but realistically, it is part of the job. No one wants to do dishes, but we teach them to do dishes because it is a life skill they need. No one likes losing, but check out the question about letting a toddler lose or not. If you value teaching the language to your kids, they'll understand that, even if it does annoy them at times, they'll feel the love behind your choice.