Hi Chainoadau93
Yes, you need tickets for you and your kids in Italy. No, Swiss Cards are not valid in this country. I suggest to buy these tickets separately:
— Florence – Milano – Chiasso (border station) on Trenitalia.com or in Trenitalia app. Some discounts are probably also available for families (FrecciaFAMILY and Bimbi gratis):
https://www.trenitalia.com/en/offers/children-s-discount.html
— Chiasso – Zurich on sbb.ch or in SBB Mobile app with your Half Fare and Family Cards.
Kind regards
Danhiel