Should be super simple to prove... Likely they both have taxpayer subsidized smart phones which ping a trace everywhere they go - should be easy to pull up the track. There is likely cameras wherever they claim they shopped, as well as other cameras along the route that they took there and back, again, should be easy to pull that footage.
And if ANY of it comes back showing that, well, she’s lying, then put the cuffs on her and haul her off to jail - start with impeding an investigation - if she doesn’t want to plead out to that, I’m more than good with accessory to murder charges.
But the KEY to that is spend the manpower and absolutely go over all that footage and cell phone data. Show that you went every extra inch to confirm the mother’s claims. It’ll save a whole lot of hassle when the death penalty appeals come down the pipe.
That would be precious if their OBAMA PHONES showed where he was!!