It probably would be best for your neighbor to cover him/herself and have the yard secured, but your child is your responsibility, and thus your yard should be the secured one.
Also, that should be regardless of the pool issue. You could get your neighbors to put a lock on the pool - but what about your kid possibly getting out of the yard, into the street, etc etc etc.
If you are concerned about the impression you are making, why not just say hello to the neighbors and let them know you have a little one, and that's why you are getting new fencing? Trust me, saying "hi, please let me install something on your property" would make a FAR worse impression.
Mom to two intact boys, born at home. DS1 11/07, DS2 9/10