You'll be sharing quite a bit of financial info with your children when you file FAFSA forms for college applications. SSNs included.
I imagine your kids will also discover your filing system for birth certificates and such when they're getting jobs at 16.
The inescapable truth, though, is that the mom should have been getting 1099 forms from DK so there's no way she could not have been a willing participant...
There is a potential reality that it was a February (1099 mailer) discovery and she tried to clean up the mess after the fact. ("HUNTER DECKERS! What have you been doing!?")