She wants to take S6 and go stay with her parents in another country for one month to clear her mind. This is possible due to the online schooling that S6 has; she will be paying for her trip expenses while I will be covering S6's costs. I think that will be very beneficial for her mental health to do that, however I will not be happy not seeing my child for a month.
Strategically, one of the first things I did when splitting with my ex-wife, was put a restraining order on her leaving the country with the kids. What if she never returned them? If this were even another state, a month without you would look bad, because it's good start to establishing a status quo of mom being the primary parent.
Emotionally, is your S6 okay with not seeing you for a month?! Has this happened before? Granted, there are naval families, but at that age, courts often rule even weekly custody changes are too hard on the children.
Anyway, I wouldn't agree to this, but think through your situation and how much you still trust this woman?