Dates

All other things being equal, I'd certainly do Rome and/or Sorrento in late Sept/early October over doing either in August. August is going to be hot and crowded. Late Sept should still be quite nice. Both weather and crowds would be worse in August.

Absolutely late Sept and into Oct. it will still be warm in Sept and just approaching needing a light sweater or jacket in the evenings in Oct. Good that you can devote 6 nights to each location and are not bouncing around all over.

will it be hot enough to swim and sun bake in late Sept - early Oct? I do like hot weather 25-30 C
Also can anyone recommend romantic place to stay with great views and preferably a pool for our wedding anniversary?

The problem is that you are highly likely in August to have temps higher than 30C, possibly far higher. You can take a look at August weather in recent years on Timeanddate.com . I just looked at 2018 and have linked to that year; you should go back several years to get a better picture of what you might expect. This year high temps were at or above 31C August 16-24 and again on August 29.

August 2017 was considerably worse. I've traveled through that kind of heat in Italy, Spain and France, and it wipes you out. You want to be outdoors, sightseeing, not hunkered down in your air conditioned hotel room.

Since this is your first trip to Europe, you may not be fully aware how many places will not be air conditioned. You cannot assume you will find air conditioning in all bars, cafes, restaurants and museums. (Hint: For stores and eating/drinking establishments, look for a closed front door.) Some places in each category will be air conditioned; some will not. It's not totally a joke when tourists laughingly say they have retreated to the frozen-food section of a supermarket to cool off.