One thing that I don't think has been discussed--if mom let dad raise Gabriel, not only would she have the stigma of not raising her own child, she'd have to pay child support. If she managed to give him up for adoption, legally or not, no child support.
I'm holding out hope that he's alive. I once dealt with a similar case--mom crossed state lines, lied to that state court, and managed to terminate rights to the child and get the child adopted. Dad (my firm's client) found out, and managed to overturn the adoption and get his child back. Years later mom finally voluntarily terminated her rights, and dad and child are doing very, very well.
If Gabriel is with another couple, I do feel for them. In the case I dealt with, the adoptive "parents" thought they were legally adopting a child, and then had to give him up. I imagine it was quite difficult for them (although they did do some pretty underhanded things, like trying to get dad fired, etc. so that they could 'win' in court).