You're misunderstanding. I don't have an issue with someone taking an advocacy role for one issue but not another. The issue here is that she doesn't care about the negative effects of her advocacy. She is ok with someone losing his kids because he gave a get right away as she is advocating. Even worse, she thinks someone should give up his kids because someone else is unfairly withholding a get.
She's against using a get as leverage and is making a hard red line around that. Are there potentially negative effects from such a policy? Absolutely. But likewise, she is saying that allowing a get to be used as leverage in some instances will cause agunos, and that is her priority. A guy "losing his kids" is an entirely different battle. Again, I understand if you disagree, but it's a legitimate position to hold. The way the question was framed, as an extreme hypothetical with no basis in reality, she could have actually said "in that narrow hypothetical which will never happen, I'd agree" and then everyone would have walked away happy. But this issue is never going to be that clear and any time the question of withholding a get comes up by definition means the case is not clear cut. It is messy. Creating red lines around certain areas, such as not being able to use a get as leverage, is understandable.
It would be wonderful if you could make a similar red line around using kids as leverage. But much the same as she can't change the fact that some men will use a get as leverage, I doubt there is a way to stop women using children as leverage.