Destiny does not have dedicated servers, instead they run P2P, which means a member of your fireteam hosts the party and is not always the fire team leader.
So it's usually the case where the host cannot handle the team on their connection.
I'd suggest having each member run through the Network troubleshooting guide :https://www.bungie.net/en/help/article/11930
Also ensure that none of your team are on wifi as this is not recommended for Destiny.
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Ok, thanks for replying - this was an LFG team, so not sure if any of what you said was the case but will try in the future.