It is most certainly possible if you and your wife and maybe even a daughter or 2 can sign up for 1-2 credit cards each to earn miles to fly.
For economy you and your wife getting 2 cards each could equal around 190k miles which would pay for 3 economy roundtrip tickets
(60k united miles each or possibly 50k AA miles each)

Factor in the cost of 3 tickets and if you would rather spend that money in Italy then go the cc sign up route.

I think the tricky part comes into play when you eventually go to book the award flights on specific dates since you already booked the hotel.