Somewhat unrelated.
For all those who are playing Destiny via remote play and wants to access party system as well. following steps seems to work for me.
1) create party on vita, invite friends
2) start remote play
3) when it's searching for the ps4 wait for it to search via the Internet, while the vita is doing that, quickly return to the party system reconnect to the chat, and tab back into the remote play which should still be searching for you ps4.
4) play destiny while shouting at stupid boss design with friends.