Though Facebook has been testing multiple account support for Messenger for awhile now, it's finally making the feature official starting today. As of the most recent update, Messenger users on Android can now switch from one account to another using a single device. You can add accounts to Messenger via a new Accounts section in Settings, and you don't need to be on Facebook in order sign in.
If you're concerned about your family and friends reading your messages, there's a safeguard against that too. You'll be asked for your password the first time you switch accounts, and from there you can choose if you want it required all the time. Messages sent to a different account will prompt a new message notification, but that message will remain private until the account is switched over. If that sounds like a useful feature for your family, you can head over to Google Play to get the update right now.