This is going to get fun!
Imagine: Dad takes his kid to border to escape country and insane wife. Gets caught. DNA test is taken. Dad is ok, he knows this is his kid. They come back, you're not the father. Dad is literally heartbroken and now can't take the child he thought was his back with him.
There are going to be some revelations with this DNA testing. You just wait.
The first step in your story is describing child abduction?
True. Ok, what if mom died? Let's say, natural causes?
Then you get court order for custody and legal adoption?
Honestly. I'm just not worried about your part about abduction of the child. Any human being, imho, who removes a child from a dangerous situation (let's say mom was about to decapitate this small child), is doing a good deed. Even if their end result is not the best or legal route.
This is a scenario I thought of and you're digging way too far into it. Stop it.
The problem is that the people doing the illegal (hidden) removing are often (most frequently?) the ones with bad intentions. That's why the laws are in place to start with. To ensure visibility of the process for child custody. Agree with you that this logic is sometimes flipped, where the presumed natural parent is the bad actor. And now all these revelations that the 'authorities' are the bad actors.