I can help on both. We stayed with our two teen girls in Florence at a B and B, Casa Tintori, very near the river Arno one bridge up from the Ponte Vecchio. The location was great, very walkable to the Duomo area on mostly pedestrian streets. The Green room was very comfortable for four, with a large double bed on one level, and two twin beds on an upper level, somewhat separated for a bit of privacy for parents and kids. It is a nice big room. One bathroom, but it was large and modern. The room has an AC but it is not powerful. We were there in late June and heat was not a problem. It is family-run and they do a good job.
http://www.casadeitintori.it/en/
As for Venice RedHouse, we rented an apartment from them for a full month in 2013, and we have another rented for next month for a shorter time. It is a local agency owned by Venetians and their prices and policies are very good. In 2013 we had the Lions House # 4 which was a very nice and modern 2-bedroom, 2 bath 4th floor apartment with a private elevator and a roof top terrace. We loved the apartment and the location, and we were able to host visitors during the month.
Next month we have a small apartment in Dorsoduro as it will just be the 2 of us, no need for anything larger. It is near the Peggy Guggenheim museum which is a good location.
If you will tell us where the apartments you are considering are located, we can vet them for you. But Venice is very compact, and location is not terrible important. And Venice Red House is a good agency. I am glad you found them in your search. Marco and Caroline are professional and reliable.