Ive done Italy at this time of year a few times. Usually end of mar til easter. The weather if fickle so you have to hope the gods are with you. Last year we were lucky. We wanted to check out the proposed site of the new portorossa Hilton in sicily. Discovered it was too far for our amount of time but did manage to drive down to puglia and then half way out, just to see the scenery. We stayed at the scandic bari and a few nites at nova yardinia (nice but nothin to do) then went to sorrento ^ then rome then home. We did this route to get as far south in the beginning of the trip (warm) the headed north and were lucky to have absolutely great weather thre whole trip. sweaters in the eves and 60-70 and sunny and warm in the afternoon.
I think this is the best bet if you want Italy. The veneto is at the base of the alps, if the fronts come from the North you end up with very cold foggy grey damp days, or that plus rain and flooding in venice. Florence can also get kinda grey and raw.
I would sugest hitting sorrento first (positano, capri, pompeii day trips etc. then head up to rome and hope its warm. Rent a Car with college age kids you'll have a blast. And self parking at the Rome Hilton is the only reasonable thing on the menu

BTW the portorosa is supposed to be open this spring and its not nec to use the amex awards its a 20k a nite one. we will be there til easter next year maybe we will run into each other

Btw Rome is my favorite city in the world. but if you dont need it. and have extra drivers sicily for 4 nites and sorrento for 4 is excellent. Puglia in the spring is really outrageous. All the fruit trees are in full bloom,and the red poppies and wildflowers carpet the valleys. Its gorgeous Like so cal or napa in spring and for what its worth its an 11hr drive from rome to there. similar to seattle-napa