Without going into a complex chemical discussion of mordants and dyes, I thought I'd share a neat video for a craft you can do with your kids. It's in the link below.
Onion skins have been used for years as a dye, I remember reading about Jewish prisoners in WW 2 who tried to brighten up the barracks they lived in by dyeing the curtains with onion skins. It's a very simple process of boiling the skins in water and soaking the fabric, or in this case an Easter egg, and allowing it to cool. It's time consuming but that's about it. The process is the same for other kitchen ingredients like red cabbage and turmeric as well. Is it suitable for kids? Yes, with some adult supervision for the boiling part. You will be sacrificing a pair of stockings/pantyhose, some eggs (white work best but use what you've got) and some flowers and leaves for decoration but it's a fun and interesting craft. I don't recommend using beets for the boiling method. Their intense colour will bleed past any decorations you use so they really don't work for this application but keep reading because I have a suggestion below. You can use a tsp of salt and vinegar in with your onion skins to help set the dye but it's not necessary. You're not looking to have these eggs last forever, they're still boiled eggs at the end of the day and won't last more than a few days as decorations.
There are lots of other vegetable dyes you can research and experiment with once you've tried this. Using different mordants such as lye, salt petre, ammonia, vinegar etc can change colours quite dramatically and it's fun to wonder how our ancestors figured these things out. You might want to try melting a little wax and painting designs on your eggs with the wax too. Once the wax is cooled you could dip your egg into some puréed or boiled and cooled beet or other fruit juice and see your designs magically appear.
Have fun with this craft and a very happy Easter from all of us at Humblebee Farm.