The only theory I can think of that ties all the facts together is that Deborah arranged the kidnapping herself, so that she could make a clean break with Jeremy. This presupposes, however, that she knew someone who was willing to take the child and squirrel her away until the case went cold. It certainly wouldn't be a very intelligent thing to do, but then, Deborah comes across as a bit wanting in the quality, as well as being something of a schemer.
And where would DB go? She has no job, no money, no car, no driver's license. Would a family member be willing and able to support her and two children? JI would have an excellent chance at getting custody, especially with her drinking and the baby gone missing on her watch. If anything, JI would be more likely to want to get away from DB, IMHO.