Cherry eyes, or prolapsed glands of the 3rd eyelids, CAN be a heritable condition.
In the ACVO-CERF (ACVO is the american college of veterinary opthalmologists) guide, breeding advice is "Breeder's Option" which means that the dog should not be bred to another dog without careful review of the pedigree to ensure that you are not doubling up on genetic predisposition.
I certainly hope when you say you had the cherry eye removed, you mean that it was surgically corrected. If the cherry eye was actually removed, it can lead to problems down the road such as KCS or "dry eye." There are several different surgies done to correct the problem.
Let me know if you have any questions or concerns.
Have I left you unhappy with the info I gave you? You left me feedback that was less than positive. Your comment stated that "I confirmed what 2 other vets have told you." Is it possible that I and the other 2 are giving you the "right" answer?
If you have/had concerns, I wish you would have contacted me prior to leaving me less than positive feedback.