An update:
I just went out this morning at daybreak to the mail box for the news paper and walked through the orchard past the apple tree where one of the eggs was buried and all the mulch was torn up around that tree only. Something came in the night and went right to that particular tree and looked for the egg. I figure it has to be a fox or coyote since they are both canines and dogs bury bones for a future meal. Because it happened at night it eliminated a turkey. I haven't seen or smelled any skunks this year and the foxes and coyotes which are abundant keep their numbers low. We do have otters and mink nearby but I doubt that they would bury an egg. So far nothing touched the flower garden where the second egg was found.