John 3:16 comes to mind first, along with Romans 5:8
Neither verse shows proof of the belief.
Who is assuming those in Hell are His "sons" Certainly not I! You took my analogy someplace not intended, as all imperfect analogies seem to end up.
Let me see...Jesus commands US to love even our own enemies which He describes as a "perfect" love...yet He loves His enemies imperfectly?
Ok.
First, your analogy was about you sitting as God in judgment upon your own son. God did do that very event at the cross. It is that you consider God overlooked the sin of His own Son and let His "perfect love" extend even through death and Hell. That is not Scriptural. When Christ rose He said to the woman, "Do not touch me." signifying He had yet to appear before the Father and there was the unfinished business of redemption and restoration/glorification. Your analogy failed.
Second, by extrapolating your "perfect" love view, a believer would then be obliged to even love Satan and demonic forces.
Did Peter love Christ? Not "perfectly" but only as in friendship.
Joh 21:15 So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou (agapao) me more than these? He saith unto him, Yea, Lord; thou knowest that I love (phileo) thee. He saith unto him, Feed my lambs.
16 He saith to him again the second time, Simon, son of Jonas, lovest thou (agapao) me? He saith unto him, Yea, Lord; thou knowest that I love(phileo) thee. He saith unto him, Feed my sheep.
17 He saith unto him the third time, Simon, son of Jonas, lovest thou (phileo) me? Peter was grieved because he said unto him the third time, Lovest thou (phileo) me? And he said unto him, Lord, thou knowest all things; thou knowest that I love (phileo) thee. Jesus saith unto him, Feed my sheep.
16 He saith to him again the second time, Simon, son of Jonas, lovest thou (agapao) me? He saith unto him, Yea, Lord; thou knowest that I love(phileo) thee. He saith unto him, Feed my sheep.
17 He saith unto him the third time, Simon, son of Jonas, lovest thou (phileo) me? Peter was grieved because he said unto him the third time, Lovest thou (phileo) me? And he said unto him, Lord, thou knowest all things; thou knowest that I love (phileo) thee. Jesus saith unto him, Feed my sheep.
Christ did not demand of Peter perfect love, but honesty.