I dont think its possiable to keep the coloring from there hands. while I think its good for them to be messy with things like this it sure recks havoic on looking pretty in the dress the next day. as far as personalizing the eggs while coloring them you could have your kids paint them or even color on them before putting them in the dye i'm sure you have heard those idea's before so im probably not much help but hey at least I will give you a bump 
How about dying them so the color doesn't come off on hands?
We make a big deal out of wearing the gloves. (By we, I mean I)
I have three kids, I put out three different types of egg coloring kits, 24 eggs and let them go nuts. It usually turns out that they each make a variety and then have a favorite of their own, and a favorite of thier sibs.
Glue, feathers, sequins and googly eyes. Just let them go nuts and make their own creatures out of the eggs.
We never were able to dye our eggs with out dying our hands. My mum just made us stick our hands in a dilute bleach solution. The colour came off pretty easily. The gloves are also a good idea.
We would also do the more elaborage egg shells where you blow the egg out of the center of the shell through a tiny pin prick, clean it, let it dry, an decorate with "stuff". When I was a kid, we would spend hours on these eggs and they were often quite elaborate
Before there were different kits on the market, we use to use a paint brush for our eggs. It was very clean and we just used the Paas brand dye. It also made 2 dozen eggs last longer than 10 minutes. One year my husband dyed the eggs by boiling red cabbage and then adding vinegar to the water and using it for our dye. The eggs were quite dark, but didn't come off on our hands Easter day. He saw an article with several different natural ways to dye eggs. Different Tea bags can be used or onion skins for brownish tones, but little kids may not have a lot of fun with that.
Watch out for Tile floors. I know someone with Egg dye that won't come out of her grout and a few tiles in her brand new home.
Here is a Martha Stewart video on making dyed eggs with mens silk ties. Really beautiful patterns and it looks like fun. You would just need to hit your local thrift store and pick up a variety of silk ties.
http://www.marthastewart.com/portal/site/mslo/menuitem.017db2225a7627b8510467a2b5900aa0/?vgnextoid=92f9cf380e1dd010VgnVCM1000005b09a00aRCRD&vgnextchannel=92f9cf380e1dd010VgnVCM1000005b09a00aRCRD&rsc=videohome&lastnavigatedchannel=c479cf380e1dd010VgnVCM1000005b09a00aRCRD
Here is a Martha Stewart video on making dyed eggs with mens silk ties. Really beautiful patterns and it looks like fun. You would just need to hit your local thrift store and pick up a variety of silk ties.
http://www.marthastewart.com/portal/site/mslo/menuitem.017db2225a7627b8510467a2b5900aa0/?vgnextoid=92f9cf380e1dd010VgnVCM1000005b09a00aRCRD&vgnextchannel=92f9cf380e1dd010VgnVCM1000005b09a00aRCRD&rsc=videohome&lastnavigatedchannel=c479cf380e1dd010VgnVCM1000005b09a00aRCRD
Ew, but then wouldn't you have to worry with old stranger neck sweat getting on the eggs? I know the ties should be laundered, but still.
Do you eat the egg shells?
The color only transfers to the shell, not the egg. And I would imagine the boiling water and vinegar might kill the bacteria anyway. You only use the wide end or bottom of the tie, not the narrow part that goes around the neck, and anyway, that part goes under the shirt collar, it doesn't touch the skin. 
My kids really like using the clear crayon to make a design and then brush of the wax prior to dying....I know this is really basic and old fashioned but it works! 
Another thing is to dye 1/2 green and then the other 1/2 blue and let it dry....then we paint a tree, flowers and a bird in the sky with the green serving as the grass and the blue for the sky....that is my favorite (because Mom has been known to spend hours on one egg - lol)
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