I wouldn't worry much about the seat request card, as there's officially a seat but the gate has the flexibility to keep families together. If the flight checks in over capacity - zeroes don't always mean overbooked, sometimes a buffer for misconnects - the airline will solicit volunteers before going to IDB.

In my travels, I've only been on a single flight that I've known has gone IDB (as I usually get to a VDB offer I will accept), and that was profoundly extenuating circumstances - aircraft type, heavy fuel load for heavy cargo, near maximum range with heavy headwinds, on a short runway on a 100+ degree today. Half the plane was not allowed to board, and I only got on because I gave HP $150 on the old "First UP" program.