So what seems to work for me and my wife somewhat consistantly when we have this issue is we both close the application first, then we both turn off the ps4 (not restart) then we turn back on. Then we join a psn chat lobby together, then we start destiny. So far it works.
Edit: also try logging out of destiny and then closing the app.
The problem seems to persist the most when one of our consoles had been in rest mode.
Hope this helps
Edit: if this helped you throw me a like or comment below