So, this is a sport so there's always going to be an element of movement, but it depends on the opponent. I know older people who play and barely move their feet, they either have incredible court placement or they play against other older people who barely move, and they agree not to play drop shots before the game.
If you're looking to play more generally, they're better off playing on the right. Left-sided players are expected to cover 65%+ of the court, as their forehand is in the middle of the court, so it's easier for them to hit balls that come down the tee.
As the other player on their team, you should be ready to cover a lot of ground, particularly if you make it to the net. If your partner doesn't like moving when they're facing forward, they really won't like moving backwards, so chances are you'll be covering for them when they get lobbed. Slow the game down, be prepared to play a high lob back to give yourself time to get back into position.
"If your partner doesn't like moving when they're facing forward, they really won't like moving backwards, so chances are you'll be covering for them when they get lobbed." - That is very well put and what I've been experiencing :)
Thank you very much for the inputs, I will try to take over the game and play more left!