I'm guessing you missed something reading the pub, or just haven't got to it yet. the IRS definition of "custodial parent" is what matters for tax purposes.
The parent whose house at whom the child slept for more than 182 nights, is the one that gets to claim them as the custodial parent. Now if the separation occurred after the middle of the year, then it's the parent at whose house the child slept the most nights. The pub also covers temporary absences, such as if the child slept over with a friend one night, for example.
The thing to keep in mind here, is what matters is what "actually occurred", and it doesn't matter what any court order says. Generally, you only have to prove your claim to the IRS if they ask for it, or if both of you claim the child. IN case of the latter, that would be reason for the parent who meets the IRS requirements, would have to prove it. Generally that's easy to do with things like school or daycare attendance records. IN particular, most daycare facilities keep track of just who drops the child off, and who picks them up each day.
