There was some confusion at one point about playing on multiple accounts but most of it's been cleared up by now so I don't see how people still manage to confuse this.
When it comes to multiple accounts, there's two contexts this falls into:
- one person playing multiple accounts simultaneously (A.K.A. "Multiboxing")
- a group of friends or family each playing their own account all at the same time.
The two are vastly different in terms of what's allowed and what's punishable by account interruption or permaban. If you're one person whose registered multiple accounts and will be playing two or more accounts simultaneously, that's considered a form of multiboxing. If you registered one account for yourself and your friends or family have also registered accounts and all of you will be playing at the same time but on each of your respective accounts, you're not multiboxing.
The latter (Friends and family playing simultaneously) is perfectly fine. As long as each person is playing their own unique account, you have nothing to worry about; you, your spouse, your children, and your friends can all be playing at the same time without fear of getting banned. The server's anti-cheat software doesn't ban multiple people playing from a single IP.
The former (One person playing multiple accounts, AKA the multiboxer) must be more careful however as there are rules in place for multiboxing. One person playing multiple accounts is permitted for certain things like item/gear crafting, item trading and banking, and enchanting. In other words, you can have two or more accounts, one to act as a extra bank for items, and one for alternate professions to create yourself items/gear or enchant your gear. However, using two or more accounts with one set to /follow the other to power level, farm materials or instances, etc. is not allowed and can lead to a ban of one of the two characters and if repeated, both characters banned.
Either way, the server's anti-cheat software also will not ban multiboxers. Even if you were playing on two or more accounts yourself, you don't have to worry about getting banned by the server because there are legitimate reasons for having two or more accounts online at the same time. Multiboxing has to be investigated by GMs to determine if an offense is taking place, meaning you have to be seen and reported by other players.
tl;dr: You, your wife, and your son are all fine to play online together. The server's not going to ban any of your accounts for all playing online at the same time from the same IP.