From the NY Consulate website:
"U.S. birth/marriage/death records must bear an Apostille [...] Petition for naturalization and/or “no recordâ€

I believe your mom is not at risk of losing her US citizenship by having her Italian citizenship recognized and I believe there is no law in Italy that prevents her to apply for both Italian and US citizenship.

http://travel.state.gov/travel/cis_pa_t ... _1753.html