254 Euros at the Westin Paris for a room for 2. 2 rooms = 508 Euros.
224 Euros at the Westin Excelsior Rome, room for 2. 2 rooms = 448 Euros.
230 Euros at the Westin Excelsior Florence, room for 2. 2 rooms = 460 Euros.

Probably not what the OP had in mind!

If you want to use hotel points for rooms in those cities, you will most likely need 2 rooms for 4 people. Most hotel rooms are tiny, with one queen or king bed, or two twin beds. They'll tell you they have fire code restrictions, or that there isn't physical room for rollaway beds. Most Europeans with kids will rent condos, vacation homes, or camp.

Occasionally you'll find a Marriott, Hilton, or Holiday Inn with two double beds in a room, but not in Paris, Rome, or Florence (I've looked as I have kids too). Check the max capacity in the hotel rooms where you want to stay as they will probably be enforced.

I would say apply for as many hotel points as you can, and plan to rent a condo in one of those cities. Florence is a difficult city on points, the Hiltons, Marriotts, Holiday Inns, and Sheratons are poorly located for a tourist.