I cannot over emphasize the importance of where you get your African grey parrot.
Yes, African greys can be skittish and high strung. However, that is less likely with greys that are well socialized. Socialization lays a strong foundation of trust, which makes for a happy life for a companion animal.
Additionally, excellent aviculturists and pet stores let their baby birds fledge, allowing them to develop the confidence of mastering a fundamental avian survival skill — flying. Even if their wing feathers are trimmed for safety in the human habitat, parrots that fledge tend to maintain that high level of self-assurance. I believe exceptional aviculturists also allow parrots to wean normally, neither selling unweaned birds, nor “force-weaning” to push babies into food independence before they are ready.
A second critical issue involves your children, and this one may be harder to analyze. Evaluate the steadiness of your children, the activity levels and layout of your household. Kids tend to move fast and make loud noises that can frighten parrots of all species. The parrots’ fear often causes aggression.
Is there a good place in your home for the cage so the parrot is not too isolated, but is “out of the line of fire” of high-energy kid activities? Can you teach your children to understand and respect the parrot’s needs? If you are unsure or the answer is no, then I would respectfully suggest you wait a few years, allowing your children a little more maturation prior to getting a parrot.
Also consider what you want from a parrot. Why do you want a grey? If your interest has to do with talking potential, rethink this issue. Psittacines are intelligent, incredibly long-lived creatures, and their talking potential is a minor attraction over the long run. As an alternative, Amazons and conures are reputed to be more resilient than African greys. Since they are also generally noisier, they should fit right into a happy, boisterous family.
One last note: Any parrot is capable of biting, especially if kids frighten it and do not respect its boundaries. What will you do if one of your children is badly bitten by your parrot? In a household where a child continually pokes fingers through a grey’s cage bars and the owner does not erect barriers, it would hardly be fair when the stressed bird finally bites the child’s finger badly enough to require reparative surgery that the grey loses its home.