I’m an Italian citizen. I want to travel to and live in Switzerland with my children, who have card residence eu limite from Italy. Do they require a visa or are they covered under free movement?
To live in Switzerland you need a residence permit, not a visa. As an Italian you can freely travel to Switzerland for the purpose of tourisme of short business visits, and your family can accompany you. Normally you will not even encounter passport control when crossing the border.
But to live in Switzerland you will need to get a residence permit. And for that you will need to meet the conditions for a permit. You will need to apply for this permit in the Canton you intend to live. The procedures you can find on their website.
Your first job however will be to find a job. Have you started on this?