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The actual regulations say this:


For purposes of subparagraph (1)(iv) of this paragraph, an individual’s spouse is not a member of the household during a taxable year if such household does not constitute such spouse’s place of abode at any time during such year. An individual’s spouse will be considered to be a member of the household during temporary absences from the household due to special circumstances. A nonpermanent failure to occupy such household as his abode by reason of illness, education, business, vacation, or military service shall be considered a mere temporary absence due to special circumstances.

 
 A “household“ is not simply an apartment, house, or other physical location. Two people living apart might still be considered to be members of the same household depending on their activities and relationship.  If you are reasonably happily married, sharing each other’s company, planning joint family activities like vacations or visiting relatives together, coordinating your children’s schools, and other similar activities, an IRS auditor may consider you to be part of one household, with one spouse temporarily absent due to work.
 
Most taxpayers are not audited. If you are audited, the burden of proof is on you to prove every deduction, dependent, or other claim that you made on your tax return; the IRS does not have to prove your tax return is incorrect, you have to prove your tax return is correct.  

If you think you can prove that you have two completely separate households, and it is not the case that one of you is temporarily absent due to work but truly creating separate households, you might reasonably succeed in your claim. It’s a risk that you will have to decide to take. Under the circumstances, I think you would be unlikely to succeed, you may wish to hire your own professional expert to review your situation.