It's never wrong to take a mental health day when needed. Ever. I hope everything turns out well and they find her unharmed.
If you're getting to a point where you need to take a day away from everything. And by everything I mean work, family, church...then do it and don't apologize for it.
If your employer gives you crap over it. Find a new employer.
I so wish we had the cure for the real pandemic of mental illness. Breaks my heart.