Sometimes I make a noodle "omelette" - its not strictly an omelette but hey
Pre-cook the noodles, sautee off some onion, garlic, ginger and maybe some scallions (white part), slivered capsicum, bit of slivered ham, or some left-over diced chicken. Then mix with the noodles, S&P, add beaten egg/s (depending how much you're doing) and fry tossing over half way till its done - little bit crispy on the outside is nice. These are nice on their own - its not very asian, but my tribe like them with ketchup! I have mine with some bottled oyster sauce over the top. Its a different egg start to the day.
Also, depending on the age of your kids, they could help and choose their ingredients, and even do it themselves with supervision. Just have a range of ingredients prepared - they'll prob experiment with some interesting combinations - and weird results - but that's the joy of learning to cook