On YT You can make live stream not public. Only those who have link to this stream will be able to watch it. I've never done live straming on FB but i think that it also can be set up to allow to watch this stream for specific people.
Setting up an rmtp server is fairly easy. In Linux this guide would be ok
How to set up your own private RTMP server using nginx or some videos on YT if You like to set it up in Windows - this one for example
If it's only 1 mile, maybe it will be possible, to link second remote to
Mavic 2 Pro and it will be possible to watch live feed from drone on phone/tablet connected to this second remote.
There are some wireless video transmission systems, but i guess they won't be cheap.