Originally Posted by
JamesBigglesworth
Entry *into* and exit *from* the Schengen area is supposed to be recorded and, IME, usually is by every member except Italy. Movement *within* the area isn't recorded by anyone, generally. The entry into Italy should have been recorded by the Italians, Italian passport or not.
National entry/exit recording systems is not the same thing as a Schengen-wide entry/exit recording system. The Schengen-wide entry-exit system isn't up and running yet, and the PNR Directive is not (yet) being lawfully used toward a Schengen-wide entry-exit recording system.
National entry-exit register systems may be relevant to the OP's child if the child entered into and exited from the Schengen zone using airports in the same country for entry into and exit from the Schengen zone, but I doubt that anyone at the Schengen ports of entry/exit would care if the accompanying adult's docs and presence appear legitimate. VIS won't be of relevance, and SIS is highly unlikely to be relevance to tracking of the entry and exit of the OP's child.
If for some reason there is a need to seek the history of legal entry/exit/stay history in the Schengen zone, it's often a very manual job to try to piece it together from entry and exit records and at times it's not even possible to get the complete history for some people because national registers aren't Schengen-wide registers. This comes up, for example, when people in some parts of the Schengen area are dealing with naturalization, citizenship-by-descent issues, residency issues and so on.