How is she obstructing justice ?
I don't know. But, Kaine is using the word obstruction so he knows, and that's an odd word to use in that context so I'm thinking it's being bandied about to appear in his current verbal vernacular.
I can speculate that it has something to do with her whereabouts/timeline the morning Kyron went missing, or that perhaps an item was noticed missing from their home, like a lg picnic cooler or something else mundane of a good size that could be misused for something and she won't tell what she did with it.
Her not telling her whereabouts is obstructing the investigation.
Them leaving her out of jail hasn't led to her inadvertently leading them to Kyron, which was probably hoped for.
They've stripped her of her child, her reputation, her capacity for earning a living utilizing her college degree, and now her home and still she hasn't cracked.
LE isn't going to stop! Her lawyer kept her from having to go in front of the judge thusfar but she'll have to - I think - if they bring more serious charges.
I don't thnk they're going to leave it alone now that she's moved away. They're going to continue hammering away until they find Kyron.
So, Kaine saying obstruction is the key to that. JMO