But MrsNarcissist - Can't you see ...
The overwhelming response to your OP is "Yes, staying nearby is the optimal solution". Come on, you knew it would be.
Why? Because that's how the majority of us think.
And likewise, you say we haven't talked about putting the dc first ... for heaven's sake ... it's so much of a given that women do this it's a fundamental premiss.
So why should you cousin's ex be so radically different?
You say you "think" - you aren't thinking, you're imagining, because you don't know, and you can't know because you have no observable facts to know with. In cases of marital break-up, (including those involving abuse,) that's often the case for those outside.
The questionis; what are you using to "think" with? You're putting a lot of suppositions in place of facts.
Why not start with the supposition that your cousin's ex actually thinks like the majority of respondents to your OP?
I really mean that "Why?". Because, while your cousins ex may be a loon, statistically it is more likely that she isn't, and has followed the same thought-processes as the rest of us.
So, statistically, you should be pondering why she's moved, and then your reasoning would have taken you in a completely different direction.
I'm sorry to go on about this, and after this ... perhaps inappropriate ... rant, I promise to scoot off. But the thing is, I think that what you're using to do your thinking with is a widely held cultural premiss that thinks women are a bit crap and are double crap if they leave marriages and steal the children. Which flies completely in the face of what we do know about women leaving relationship and how they think about their children.
It acts to subtly distance women from their emotions and their sense of their rights and their autonomy. It helps to lock a lot of women into less than optimal situations. It may not be the case here, but it's a prevailing mind-set.
And I have to return to the "not putting dc first". Please do some reading. Women in relationships generally weigh up their own lives against that of their dc and come to the conclusion that dc weigh more. And those that don't come in for ENORMOUS cultural opprobrium - of which your post seems to me to be an example.
It all adds up to making it very difficult for women with dc to keep a tight hold on their self-hood and their autonomy. And I'll be honest, I think it helps to enable abusers in those relationships where abuse does go on.
No, I'm not saying that happened in this case. Hell, I don't know. But the attitude of blaming the woman, of constantly negating a mother's autonomy is Not Helpful. An Must Stop. Now.
And yes, of course I think it's optimal for the parents to stay geographically close after a break-up. But then, most of us do.