Navigating EU Immigration Rules to move to Germany!

As a non-EU-citizen, she is only allowed visits to the Schengen area of 90 days duration in any 6months period.

If she is here longer than that, she does no longer have a valid Schengen visa and thus cannot visit any Schengen country.

That she has applied for an Italian residence permit (which is strictly national) and, through that, might have gotten permission to stay in Italy longer, makes no difference in other countries (including Germany), because Italian law does not apply there.

So, in short: No, she cannot visit Germany!

I recommend she applies for a Family Reunion Visa at the German embassy in Italy and relocates only after that is issued.

Like Beppi menitoned, I think officially she cannot come to Germany yet. If she gets the national visa, then her time is unlimited in Italy and she could come to Germany on this basis for 90 days. Thus not likley a punishment or big risk of deportation - but it could mean a hassle to deal with. But there is no normal check at the borders to go from Italy to Germany,

I think if anything official came up, they would understand the situation and that there is no intent to do anything wrong. But best to do as Beppi suggested and ask at the Geman embassy or consulate about a German family reunion visa.