Satellite service mixed with app in different location

I have been asked to relocate for work. We will be keeping our current home on West Coast and buying another in the South. Obviously, I do not want to pay for two accounts. I would like to keep current satellite service on West Coast due to questionable internet speeds and use App in other house (Fiber available).

Is this allowed? Would all of our channels and premiums be available in both locations?

How much are the Gemini Air boxes if I'd like to use the remote?

(When I asked about it a couple of years ago, I believe they said I would have to go with DirecTV Stream.)