I am living near MXP for a few years, its quite nice and you can rent a house near the lake for about 800-1000€ at the size you will need with 3 kids.
In Varese there is an European School, which is quite good when your kids have to go to school.
Maybe Milan ist better for you, because the summer gets quite hot in Italy and I always have the impression that when you are not used to it 34° in Milan are better than in Rome.