I can understand why you would not want to share your garden with strangers but with 16 different families already having access that is a lot more the I would fell comfortable allowing access to an area my daughter plays in unsupervised and she is seven. Maybe it will not be as bad as you think. You might get the occasional renter who behaves badly but I would suspect that except for those rare exceptions must people only use the garden area the same way you do. You might even get lucky and meet the occasional new friend. My uncle rents out a beach house and except for the occasional broken dish or picture frame he never has issues.

I would be very quick to call the police though if anyone is making a nuisance of themselves. I would also take the precaution of putting extra security on any access to the patio. I assume these people are putting down some sort of security deposits, I know I had to when I have done similar rentals, and if they damage anything or leave messes take that up with the owner of the flat. Usually some sort of cleaning fee is required, try and get messes left in the garden are included. It would probably be a good idea to express your concerns with new owner now. We rented a house in the mountains this summer and they had a list of things we were not supposed to do like mess with the beaver damn or go exploring to far behind the house because it was surrounded by private property.

I know this comes off sounding like I am saying you are over reacting and that isn't the what I mean, there just doesn't seem like much you can about it and maybe it will not be a bad as you think. Most people are decent and try to respect the rights of others. Of course I may simply think that because I live in Texas and that is the way most of the people outside of the yankee infested cities act