Our apple trees are about 5 years old and have not provided any harvest. The trunks are about 3 inches in diameter and 8 feet tall. The problem arrives mid summer. The foliage is a dark leafy green and the tree has small fruit. Overnight there appears black spots that have a yellow circle around it. The fruit gets black spots and becomes pitted. The apples do not increase in size. The largest was approximately 3 inches in diameter. I try to trim back the trees in January or February in height as well as branches. My sister thought we should also get rid of the grass that grows at the base of the trees since they are in the middle of our yard. Any advice would be very appreciated.

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.