it's just manga logic ig. But be fr, how does that even work. When I was reading the explanation, I was still confused as hell. Why would the material grandfather go out of his way to do all of that. Your comment about going to another country, I don't think it's really possible if her grandfather is that influential, cuz like can't he find out before hand? Also most things she has is connected to him or at least under his influence so finding someone who would risk it is...questionable.
and about going to the police, he could had just say it's family issues and make it smaller then it is by controlling the police force with money.(if he's that influential)
But I would also think that he would have threated to block anyway for them to go out of the country and have any jobs if so.
police force can be corrupted after all, another thing. The grandfather most likely has outside kids if he treat them like that. cuz no way in hell a normal rich man treat their only child's kid like that even if they mess up in childhood. like he's only a kid and kids can mess up at times.
(I accidentally click follow, sorry)
Well, since i read (too much) Korean chaebol manhwa , i could say the grandpa indeed powerful. Even the father could divorce his wife, that makes it harder for them to meet. The granddad could make father fired, even go to jail and make our MC suffered. They could push their siblings to hell if needed.

I don't think, that if a mother truly loves her child, she can be forced to abandon it just because her family says so. Just f***ing go overseas if your family is so influential in your country, and go to the police if they don't allow you to... What century are they living in?! ヽ(`Д´)ノ