Our traveling style is very much relaxed....We also love to just sit
and drink wine and talk for hours.
If this is the preferred style, I don't know as I'd recommend an RS tour. It sounds as if you travel much the same as we do, and having that sort of time is why we do it independently. But it's also the reason we tend to stay longer rather than shorter in one place.
Wine country and hiking in the Cinque Terre sound right up our alley.
However, is it possible to do a day trip to Venice from Rome? The
canals sound beautiful.
Again, consider that you're going to lose a big chunk of a day moving between cities; more than that between Paris and Rome or Florence (I assume you'll fly). You'll lose some transferring between Florence and Rome as well. There is a LOT to see in Rome so you'll need every bit of your 3.5 days to barely scratch the surface. Venice is much too far away, and you really don't want to devote hours and hours to a train that you could spend sightseeing? Save it for another trip.
I'll say the same for Florence: you'll have 3 full days and are already looking at spending two of them on day trips. While smaller than Rome, there's still a lot to see so please don't cut that one short unless you know you're not interested in much that it has to offer?
The Cinque Terre: will be insanely busy in August so that might be a good thing to be aware of? Honestly, the best way to do that one is to STAY there: the golden hours are in the early mornings before the mob of day-trippers arrive, and in the evenings after they depart. Just as with Venice, I'd save that one for another another trip.
With the exception of a train mentioned in a previous thread linked below (don't use the train numbers; just approx. departure times and stations) you'll also kill about 5 hours of the day or more just getting there and back to Florence.
https://community.ricksteves.com/travel-forum/italy/florence-to-cinque-terre-and-back-an-overlooked-option
You can take a 5-minute train from Santa Maria Novella to Campo di Marte but the transfer time is another 25 minutes so.
I'm not trying to throw a wet blanket on your enthusiasm (really, I'm not!) but I see you already piling too much on that will leave you little for the relaxing times you're so looking forward to! If you want to take a day trip from Florence - and I don't know as I'd do more than one - you might consider Lucca or Siena instead? Both take less time to get to than the CT.