I tried to PM you this, but it wouldn't let me. Anyway, here are my thoughts in response to your message:
Are you NJ residents? I assume he did not receive a Type 7 either? Either way, first, there is absolutely nothing at all wrong with a full-ride from Rutgers. I suspect you don't appreciate the value of that regardless of anything else. That is plenty to work with going forward and does not include, if he doesn't want it to, the added requirement of military service. If he does, though, so much the better. The point is he doesn't NEED an AFROTC scholarship with a full-ride to Rutgers.
Second, I happen to be a (two-time) Notre Dame grad (3-year AROTC winner from way, way back). I take it your son was accepted to ND? If he was, I would encourage him to get in touch with someone at ND's AFROTC unit to basically make his case that he desperately wants ND but can't afford it without the ROTC scholarship. There's no telling what they might be able to do. Maybe nothing, but I wouldn't go down without going the extra mile with ND. The ROTC units there all have an excellent working relationship within the university. Perhaps with the right word from AFROTC, the university might be able to give your son some extra help for freshman year with the idea that he'd be a virtual shoo-in for an on-campus scholarship once he gets there. I'd make them tell me no before he gives up on that.