I recently got my gf a PS4 and we're having this same issue. We connect via an Apple Airport Extreme router (one via wifi and one via ethernet) that connects via cable to into a China Telecom owned modem. Note, I have no admin access to the China Telecom modem because they lock out users from accessing the settings - as such I can't tell you anything about how this device works. I have (touch wood) 100% success rate by starting the games at precisely the same time, but it's very annoying if one person is mid-game and wants to join the other. Imagine if you will I'm mid-raid and we lose a player. If I want my partner to join me, I need to quit the game and restart Destiny synchronised with her. I pessimistically suspect this will only be fixed in Destiny 2 because there is a convoluted work-around for most users, so it's not a priority for D1.

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My wife and I had the same problem until we decided to switch internet providers from AT&T to Xfinity. Destiny requires something called UPnP to be enabled on your modem or router, which is not provided on AT&T modems/gateways. What allowed us to play in the same Fireteam while we had AT&T was doing something we "lovingly" called The Ritual. As silly as this is going to sound, it worked about 80% of the time. ------- The Ritual: Go ahead and join a chat party with whoever you are intending to play with. Uninterrupted communication is absolutely important here. Step 1: The both of you have to start from the home screen. From the home screen start up Destiny AT THE SAME TIME. (IE: 1,2,3, Go!) Step 2: At the title screen, both of you have to press start AT THE SAME TIME. Step 3: At the character select screen, when you're choosing your guardian, both of you have to select your guardian AT THE SAME TIME. Step 4: When you get into orbit, select the Tower. When the both of you are ready to launch, hit LAUNCH AT THE SAME TIME Step 5: When you reach the Tower DON'T DO ANYTHING! Don't open your inventory, don't walk around, NOTHING! Just stand there until the both of you have loaded into the Tower. Step 6: After the two of you have loaded into the Tower, bring out your ghosts. At the same time, hit the button that will take you back to orbit, whether that's Y or triangle. Step 7: When the both of you get back to orbit, one of you try joining the others Fireteam. Leadership can be discussed afterwards. ------- That's it! Like I said, that would work for us about 80% of the time. I'd almost go so far as to say it works 100% of the time, it's just a matter of synchronicity (doing everything at the same time). Give that shot a couple times and see if it works. Sometimes, we would do The Ritual up to five times, depending on how badly we wanted to play Destiny. Usually the problem was that one of us would be out of sync I hope this helps!