No, the correct response is to tell that person to go fuck themselves. That is the worst kind of manipulation. I feel bad for you, using your brother's tendencies against you is a ridiculous level of evil in my opinion. It depends on your brother and your relationship with him, of course. But I would be willing to bet that she does not go through with it.

Besides, that is a very un-nuanced threat: what would happen if you called biweekly? Would she half-kill herself? What if you made it every month?