I don't know if I would worry so much about the poop from 2-3 chickens killing the yard. the chickens will do a fine job all by them selves. they will have a ball relocating the sand and bark. digging holes in the flower beds and pooping on the back porch while waiting patiently for you to come and give them treats! Fencing them in an area that your parents aren't going to freak out about all the above activities is your best bet. I too have a wonderful back yard I wanted a few chickens to wander about freely until all the above happened now they have their place and I have mine, all is well.
