How to get dog to poo in yard?

Just over a month ago we adopted a 2-yr-old Chihuahua mix from the shelter. She has settled in just fine. The only thing is that she won't poo in the yard - neither the back nor front yards. She had done it in the house, though. Every day we take her for at least two walks to the park so that she can go (she has a bowel movement 2-3 times a day). The park is not without its problems - she has gotten sick from eating stuff that people throw on the ground, she was nearly attacked by a big dog, she won't go in the wet grass after they have the sprinklers on, she is afraid of the children who play there, and she hates to walk in the rain. So, we'd like for her to go in the yard. Any ideas? We did try the pheremone spray but it has no effect. Thanks in advance!