She needs to let go of that sympathy, at least for a time, so that she can steel herself to act against her cousin’s best interests.
This is a genuinely incomprehensible view of the situation. How is it against the cousin's best interests to keep her kids safe? WHY DOES ANYONE NEED TO LOSE SYMPATHY FOR SOMEONE IN ORDER TO ENSURE THE SAFETY OF CHILDREN FROM AN ABUSER?
Your worldview is dangerously black and white. You seem to think that there are only two ways to feel about people & deal with them:
You feel good about someone. Then you have sympathy and compassion for them, you like them, you consider them good, you must agree with them, obey them, never go against their wishes, and feel like they are the best thing ever. You are never allowed to leave such a person.
You don't feel good about someone. That means youmust be angry with them and lack sympathy for them and blame them for everything. ONLY IN THIS CASE you're allowed to disagree with them, do things they don't want you to do, disobey their wishes, leave them, etc.
Your black and white worldview is dangerous for you, and dangerous for anyone else who decides to believe in it. What a ridiculous concept you are defending!!! This is beyond bad advice.. it's dangerous advice. You really have a lot of growing up to do.