I have to pull my hat off to Emmanuela who was super helpful organizing our arrival.
Since the appartment is located in the center of Florence, the real issue is with parking. She offered us to either park our car a bit further out of the city center (near her actual home) where parking is free or to go for the parking (26€/day) which is 1 minute walking distance from her appartment.
Since we were not super well organized we went for the parking and she was there to help us go through all the admin part with the parking guys.
She then showed us up to the room where she also took time to give us all the insiders tips to Florence.
Thankfully the aircon was working (a bit noisy, but you do prefer having it on in the middle of summer in Italy)
Our 2 days spent there were really nice and this, thanks to Emmanuela's tips.

Whenever we come black to Florence, we will surely try to book this flat again.