This app was mentioned in 2 comments, with an average of 1.00 upvote
What you could do is use a second app that syncs to strava to do the ride.
So have your strava app on your phone linked to your main account.
Then use something else - I use JayPS because I have a Pebble watch so I can view the time and speed etc on it using this. But then I have it set to upload when I stop the recording at the end of each ride to my strava account. So you link that to your family account.
It does mean starting and stopping two apps, but it works. I'm sure there are other apps that would work better, but I use JayPS cus of my pebble.
Alternatively, tasker could do it.... But it'd be a pain to setup.