Suzan. "recommendations" have stayed at a few sites in tuscany and around lake garda, but have never taken the caravan.
I would double check the opening times of any site you are considering as they are very much seasonal and april might be a tad early.
Figline valdarno is a big favourite of mine, just 15 miles south of florence, well placed to do all the tuscan sites, but part of the road is a litle thin and twisty, never the less a popular site.
Southern Italy? again i would stick to the higher rated sites,even if this makes them a tad dearer. As you will be traveling in low season the roads should not be too bad,although if you do go down to the almalfi coast i would suggest finding a site maybe 20 or 30 miles from the coastal road as its not ideal caravan country.
I would recommend the aosta region atleast in mid to late may.
the grand san barnard might be open,so should the little san barnard, well worth a drive to, although leave the caravan somewhere near the town of aosta, there are a few sites nearby.
What ever you do enjoy it..