I recently came across an ad on facebook for a service in the plane called 'Nanny in the clouds'. The service is exactly as it sounds...a babysitter while you are on your flight to keep your baby/child busy. How does this work? Well parents and babysitters are connected via the website, essentially if sitter is on your flight you are paired for about $20 a hour. To assist with security, flight, and picking up your baggage.
It's a cool new idea, however after traveling on more than 30 flights and three international flights mostly by myself with DMC. I don't think a sitter would help much, considering you are still sitting with your child and naturally inclined to react to any type of cry or restlessness. Plus most families are only traveling 3-4 hours to destinations and if both parents are flying you trade off duty. The website is currently on hold for now.