Mention two-body-problem in PhD applications? If so, where?
I would not do this. For faculty applications there is an argument to be made that alerting the search committee about the two-body problem gives them time to come up with solutions. A faculty candidate is a large enough investment on the part of a department/university that spousal hires/accommodations are a reasonable thing. I have never seen a PhD student, however, who is so good that the admissions committee would give the idea of offering a place to the trailing spouse a second of consideration. They might, however, decide you are not worth the effort if they know a partner is involved.