IMO It keeps Kyron in the media's attention, and thereby in the public's attention, that's how it helps. And IMO it makes Desiree look like a devoted mother who will not stop looking for her child. In contrast, there are many missing persons cases where the family is seen to do little to nothing (Susan Jacobson, Stephanie Warner, et al) and they are criticized for it.
And considering that no "trespassing" arrests were reported in this incident, Desiree was well within her first amendment rights. Her husband is a police officer, for heaven's sake. I doubt she would do something illegal in order to find out where Kyron is. I'm sure her instinct would be to put her hands around TMH's throat until she gives up what she knows. The fact that Desiree has shown such restraint is remarkable, IMO.