Ordnet.dk says it should be: et centrum, centret (eller centrummet, eller centrumet), centre (eller centrummer, eller centrumer), centrene (eller centrumene, eller centrerne).
So anyway you go it's fine!
And it also tells me you can say: være (i) centrum for NOGET. So I believe it doesn't take the definite article simply because it's a common expression.
I'm not sure that I understand the intended meaning of this sentence.
Is the danish phrase referring to the location of the kitchen within the house, or Is it referring to the cultural importance of the kitchen, within the lives of the people residing in the house?
I was given two possible answers for this: The kitchen is at the center of the house The kitchen is the center of the house
But these two sentences have different meanings.
'at the center of the house' could refer to the location OR the importance
For example My children are at the center of my life. (My life revolves around them) My children are at the center of the field (location)
If the meaning is location, then this answer should also be accepted and is the more common answer: ' The kitchen is in the center of the house'
If the meaning is only importance, then the two answers you have suggested are correct, but this becomes a confusing translation.
As far as I know, the meaning can be interpreted either way, same as in English. "The kitchen is the center of the house". Having a degree of ambiguity is important in a rich language, don't you think? :) Opens up all kinds of doors for wordplay and various connotations/interpretations. This one was probably intentionally written to suit both meanings.