Short Version: Destiny 2 does not send a UPNP discover or the packets required to open up ports to the firewall.
Extended Version: UPnP is enable on my router (Ubiquiti ER-X). UPnP, as it is configured, is working. Destiny 2 on PS4 will open the ports required for gameplay, and other PC titles (such as Warframe) are also opening their required ports. I used Wireshark and performed a packet capture during the startup, character select, and tower load phases, and not once did I see an SSDP request, or the appropriate packets sent for opening the required ports. While my wife and I can usually play together without too much issue, adding additional people to the mix can sometimes result in disconnects for random people in the fireteam.
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Hey there. Thanks for reporting your issue to us. What is your NAT type currently set to? When you play with the fireteam without your wife, do you have issues? What if your wife is with the fireteam but you're not with them?