All you need is:
a hand held blender and a tall beaker.
1 egg
200 ml sunflower oil (you can do it with olive oil but then it may taste a bit bitter)
1 tbspoon vinegar
a pinch of salt
Put the egg in the
tall beaker. Add the oil. Cover the egg with the blender without moving the blender for 30 seconds. It really is important that you do not move the blender at all. You will see how a think ribbony mayonnaise starts appearing at the bottom of the beaker. Start moving the blender up really-really slowly. If you do it slowly enough the mayonnaise will never curd. When the blender is at the top of the beaker you can then move it up and down with no worries. Add the salt and vinegar and blend again (you can now do this fast) and job done.
You can add anything to mayonnaise: mustard, garlic, tomato ketchup, tabasco and orange juice for cocktail sauce, capers and cornichons for tartare sauce...
The kids can add the ingredients to the beaker but do not let them handle the blender or you will end up with lots of curd sauce...