The apartment situation is not really a tax issue, as much as it may be a legal issue. So I'm not going to address that. You may wish to seek legal counsel on that front.
For tax purposes, the IRS has their own set of rules for who can claim dependents when it comes to separated or unmarried parent's no longer living together. It's all covered in great detail in IRS Publication 504 at https://www.irs.gov/pub/irs-pdf/p504.pdf
