Your general description of what is going on matches a fungal disease called Cedar Apple Rust (CAR). This is a disease that uses both an evergreen host (cedar or juniper) and a deciduous host (your apples) to complete it's life cycle. Late summer and fall it lives on the evergreen host. In early spring, spores float through the air finding the apple. There the spots as you describe appear. The other possibility is a disease called frog eye or black spot. you can find images of both at http://www.caf.wvu.edu/kearneysville/wvufarm8.html
Both would require spray treatments starting at bud break continuing every 5-7 days depending on product to protect the young leaves and developing fruits.
Grass right up to the trunks can be damaging if rodents living the grass are feeding on the bark and roots during the winter months. Damage to the trunk can also occur from the lawn mower and string trimmer. Even a small ring of 12-18 inches is enough. If you are feeding your lawn around the trees, this could be impacting the fruit production by stimulating vegetative growth.