Gofund has an excellent suggestion as always.
I'd like to add that all of destiny aside from orbit is P2P. Things like patrols, story and the raids run on a different kind of P2P, but it's P2P all the same so packet loss can be an issue.
I would double check that you have UPnP enabled on your router. Ensure you have nat type 1 or open nat enabled.
Make sure, if using a modem/router combo AND another router connected to that, make sure the modem is placed in bridge mode.
Make sure that the routers wifi channel is different than anything else that runs on wireless in the house. Portable house phones, nest thermostats and baby monitors to name a few.
I have several friends that this happens to on a consistent basis and can assure you it's connection related.
Good luck and let us know if there is any way we can help.