This exactly. OP, use the 'All Passports' line.
This is allowed if you are married/de-facto, but not generally for non-EU passport holders travelling with EU passport holders. Of course, the level of enforcement differs between EU entry points.
+1
Border control knows that the kids may/may not have the EU passports and luckily seem to be smart enough and know that young kids travelling solo usually are a red flag... or rare, unless if they have someone from the airline making sure they get to their parents and such.