Hey- well, I haven't "handled it" yet, but you're right, only one person can file the dependent. Sometimes people trade years, but to be fair, if it's 50/50, the person who could benefit more from it (like if she got a different tax break for something else, she could let you have this one, etc) should get it, via negotiation. You're right, you can't "split" it.
My CPA told me that unless you've been D'd this year (there are some nuances- check with a tax person- I am not sure for how long during the year you must NOT have been D'd or by when you'd have to have filed for D in the year to file separately), you still file together this year, then would file separately next year- at least that's our sitch.
When the men on the chessboard Get up and tell you where to go; And you've just had some kind of mushroom And your mind is moving slow; Go ask Alice... I think she'll know.