"What is with the mother?"
Translation:Was ist mit der Mutter?
Because the subject/object that we are asking about is the (unknown) object, which is with "the mother" (which is the indirect object part of the sentence). Indirect objects are expressed in the Dative case, so 'die' has to be changed to 'der'.
Another rule to remember is that whenever mit (with) is used, you always have to use the dative case for that part.
The rules trip me up constantly as a native English speaker trying to learn German, and it seems that it is best to learn the pronouns by rote for each gender/case.