Fastmail allows for email aliases. These aren't those addresses with a `+` on them, but rather completely different addresses. You can put the family address and generic address in your own or your wife's account and setup a filter so that email to those addresses go to separate folders automatically. That saves you $60/year. If your children don't need privacy from one another (I've no clue how old they are or how well they get along), maybe you can also group them into 1 account to save you another $90/year.

By the way, Fastmail prices are rising. One used to be able to get a free account, and the standard plan used to be $40 a year, so might be good to get them sooner rather than later to get grandfathered-in in case of upcoming price risings.