How did he get the deed in both names but the loan in just one?  Did he deed it to her after purchase?  It all sounds very convenient (like leaving the house vacant for Christmas and then moving over New Years weekend).  If that's their story and they're sticking to it, you still have to contend with the language of Section 7703, which does not say "living together" -- that's just the dumbed-down language of IRS publications.  What it says is,

"during the last 6 months of the taxable year, such individual’s spouse is not a member of such household"

An IRS auditor will probably say that the new, unoccupied house is the "household," and their temporary absence while it is being remodeled is not relevant.  Or maybe her apartment is the household; he doesn't have to be spending the night there, although I wonder if this was all just a platonic arrangement.