It's possible to run many Steem accounts from one computer. There are even some Steem platforms, like SteemPeak, that allow you to switch between different accounts on the same computer.
Obviously you need to have a good degree of trust between members of your family (I'm sure you do!) to operate in this manner. As a comparison, using a public shared computer for Steem is not advisable due to the risk of your account being hacked.