I'd go this far ~ which is certainly not amnesty ~ just enroll them in a Berlitz language program for maybe 3 months of immersion in their native tongue.
Then send them home.
I think that's only fair ~ if the government didn't want to send mom and pop back, make it up to the kid with some free schooling ~ then send him back anyway. Now he's at least "bilingual" eh!.
The kid is entitled to nothing. Still, if our overlords would buy into your proposal, I’d support it. That they would do any such thing is fantasy, of course.
You started your post ok, identfying the mess of deporting someone to a country who for all intents and purposes they never lived in. That is an estute point. But then to turn and say give that person a crash course in the language of the country where they are to be sent? That takes what you identified as a complex issue and trivializes it.
Something certainly must be done. But If anyone thinks it will be possible to deport them all just do the math. How many buses would it take just for starters? 12 million people at 50 people per bus.