Since your child has current leave therefore he is subject to immigration control and (technically) will become an overstayer after expiry of his current leave.
If you do not include him in your wife's FLR application and for any reason if your settlement application is refused after the expiry date of your leave, he will have no right of appeal (since not included). On the other hand, if your settlement application is approved then any such "overstay" will have no relevance to his registration as a British citizen.
With the above in mind, you can decide whether you wish to include the child in your wife's FLR(M) application or not.
As for your wife, read
this topic