-->This varies by country, I can only speak from the US perspective.
False
1) Custody & visitation agreements are set up by the courts and dictate a Minimum amount of time for the non-custodial parent to have Legal Right to spend with their kid(s) and any conditions/restrictions on that.
2) I am the custodial parent, so if this were true I'd still get to see my kids and would never have to speak to my ex again.
3) It's totally scary that the legal system has the following term as part of its vocabulary: "non-custodial parental kidnapping."
4) There are other Legit options, I'm sure.
Let me add, however, that the better the parents can get along afterwards, the better off the kids are.
...unless maybe one of the parents should be in jail, or similarly confined by the state.