Sorry to say, a lot of breed rescues are not going to adopt to someone with a two year old child and no yard. Yes, part of the reason is that they don't want the dog returned or let go on the street and part of the reason is they do not want to be held responsible if someone should get hurt as a result of the dog's actions. It is going to be very difficult to find someone who is going to adopt a young dog to you in your situation.
Good luck on your search for the perfect addition to your family.