Actually, Dogfish, I have an answer for your problem with them eating the turkey eggs, as well. But, please, everyone, take my following cautions (stated in CAPS) quite seriously, if you would, please.
I have found this to be highly effective. Our terrier was stealing chicken eggs every chance it had access to the coop (we let our chickens out each afternoon, leaving the coop open for the dogs to enter), but this process fixed it with just one application, which lasted a couple weeks, and then another follow-on application when she returned to try again. Hasn't happened since, even though she has free access to the coop every day.
Go get you a compressed-air type of air horn, the kind sold for use on boats. You'll find it in the boating or R.V. sections of any large store. Sometimes they're in the sporting section, as they are also sold for noise makers at sporting events. But get the big one, not the little ones; the big one has a lower, bigger sound.
Now, watch the dog carefully for the right opportunity. To be most effective, you have to be stealthy, and try to catch the dog in the act, without the dog knowing you are watching. Also, to be most effective, the dog would have never before been exposed to the loud noise of such an air horn. So, this training technique must be USED VERY SPARINGLY, or it will quickly lose effectiveness. DO NOT USE AN AIR HORN IN EARLY TRAINING OF DOGS. But, it can be an effective help aid in the final, advanced training steps of any process you are having difficulty with, if the message is "don't" rather than "do."
Just as the dog starts to pick up the egg, run up behind it and give it a loud blast for just a second or two. This essentially is giving you a huge, huge voice that the dog didn't know you had. The dog will be so stunned, it might appear anesthetized for up to thirty minutes. What I mean is it will, after the first startled reaction, be very, very calm and perfectly behaved. You might find that it stays right at your side. It will be in a frame of mind that it wants to keep you very happy. I've never seen a dog look scared with this technique...just calm and well behaved.
I have also used this for asking dogs to quit excessive barking, such as when people come to visit. (another "don't" request) However, again it has to be used just once or twice, and the rest of time rely only on your own resources and not the horn. Otherwise, the horn just becomes more of you barking back at the barkers, and the process fails. I like to say if a dog has to hear a horn more than three times in its life, you've used it too much.
To understand why this works, I suppose this could be described as "clicker training on steroids."
Good luck!
--Bryan
P.S.: I think of a caveat: I've never used this on dogs with which I have NOT done my Leadership and Trust steps with (steps one and two in the video). As I think about it, this suggestion might be suspect when used with dogs that have not given up leadership (a/k/a dominance) to you. Dogs that I work with have *always* gone through steps one and two, first thing, and this makes everything else from then on easy. It is quite possible that that would be a factor in my success with this horn approach. So, use with caution. Using it to counter barking without having those two steps down could easily backfire and fail miserably.