“In this case they are trying to embarrass him as pressure to give a Get. Also is this social pressure sanctioned by Bais Din?” “I am not saying it’s 100% prohibited to use social pressure in this case. What I am saying is that it’s a minefield, as you can lose your portion in the next world and should be avoided.”
If the Beis Din says to do so, then it is a Mitzvah to do so, and you are not allowed to worry about losing your portion in the next world. If you refuse to listen to the Beis Din, you will be greatly punished in the next world.
The concept of losing your portion in the next World for embarrassing someone should not come into the equation. The only question one should be asking is: “What does the Beis Din/Rabbanim say to do?” If you do the right thing, you will be rewarded. If you don’t, you will be punished.