Clogged sink drain...except not that simple

So my idiot Father In Law clogged the garbage disposal drain in their kitchen sink. Except that it's not that easy. The disposal itself is clear, as is the trap under the other half of the two basin sink. We already did the liquid plumber thing. And we did the plunger thing. I even took it all apart and snaked about 25' of drain pipe...still not draining. Even a little. I'm a pretty good plumber, even plumbed my entire house when we renovated in '11 so I'm fairly certain I'm not doing anything wrong, but I'm at a loss as to what can withstand the rigors of a snake and still clog the drain, and how to tame that particular dragon, once identified. Any help would be much appreciated.