Hi, we own a property in a green area, near

The right of prelazione is for those who are registered as a coltivatore diretto o azienda agricola, or have been renting the land with a standard contract.   If you are none of these and just a neighbour, then you have no right to first refusal on the land. 

Tx Modicasa! Where should you register this and what is exact the definition to be one of the two. For example, we let local farmers use our prato for free for their animals.

Thank you. 

Its not just a question of registering.   You would need to open a partita IVA, (obviously be resident and tax payer in Italy) and have no other job.   You have to get the majority of your income from your land, and this has to be demonstrable.   You have to work the land for a minimum of about 100 days per year.    You let other people use your land, so you are not the coltivatore diretto here - and you should have a  contract for the rent of your land (even at a peppercorn rent) to not lose your rights.