Can I claim my stepchild if my soon to be ex wife says no, despite paying the entire year's living expenses?

My wife and I are getting divorced, but it is not finalized and likely won't be until December or January.  She hasn't worked in almost 2 years, so I pay for all of her living expenses, including a side agreement with support money to last her until mid December so she has time to move, find a job, and start drawing paychecks 

This week, she decided to try and buck our agreement and threatened to have her brother, whom she and her child have never lived with or received any support from, claim them both so he can get the tax refund if I don't make adjustments in her favor above and beyond our previous arrangement.

Does she have the right to do that, or do I have the right to claim them both as she hasn't had a job and I paid for both of their expenses over this entire year?