OK, I understand now.
So, the problem may not be pruning, but nematodes. The soil in Florida is known for nematodes, and the roots on your rose may not be very compatible. Nematodes can attack a rose's root system and destroy it. This is why many roses that perform well in Florida are those that have been grafted onto nematode-resistant Fortuniana rootstock, rather than growing on their "own" roots as yours is. There is a specialty nursery, K and M Nursery, that provides custom grafting services using Fortuniana root stock. It might be that you can send them a cutting and they could graft it for you. There are others on the forum who know more about this than I do, since I'm located in the northeast and use a different root stock for grafted roses. Hopefully they'll weigh in here shortly.
Here's a link to K and M's website. Use the three-line menu bar in the top right corner of the home page to navigate the site (the links at the bottom of the home page don't work right now).
https://www.kandmroses.com/
By the way, it's wonderful that you have this rose that has come all the way from Italy and down through the generations of your family.