With luck and a fair wind, a Schengen decision can be made on the same day it is submitted, but for judicious planning purposes, a Schengen decision will normally be reached within 15 days of submission, and it is reasonable to assume this to be your minimum expected turn-around time.
The maximum decision time can be up to 60 days...
As a general rule, once a Schengen visa application is submitted to
the Consulate, a decision is taken by the Consulate within 15 calendar
days. This period may be extended up to 30 days or 60 days. More
information is available on our website on this page: Processing of a
Source: Frequently asked questions
The authority to extend to 30 or 60 days is given in Article 23 of the Borders Code.
Italian consulates use the Visa Facilitation Centre scheme so a personal appearance at the consulate is not required but depending upon where your family is vis-a-vis their nearest centre additional travel days may be needed to obtain a VFS appointment for enrolling their biometrics.