Can i go on a trek with my family in italy?
Of course!
The only difficulty may be when your children start to be too big to carry but are still too young to hike for long. If this is the case, you'll have to adapt your schedule to their little legs.
That said, Italians love children and that's a big plus when you're in tourist spots. Your children will always get a warm welcome.
The Great Lakes region, which provides opportunities for a variety of activities and doesn't have significant changes in elevation, can be a good destination to try out trekking with the family.