Mary dying would no doubt affect many characters. I'm torn at how it would affect Edith's relationship with her parents at first, but in the end they would definitely cling on to her as their only daughter left. As for Edith, I actually think she would be sad, because for all Mary's rudeness and snobbery, part of Edith still does feel for her as a sister (such as in that moment when Edith took Mary's hand as they remembered Sybil), and I think all this time Edith only ever wanted Mary's sisterly love.
Mary of course never thinks of Edith as a sister, not like she did Sybil. I doubt Mary will be the one dying if anyone is, but she definitely needs to be taken down a few pegs. Her eyes need to be open about Edith's heart and character. She simply cannot - or chooses to overlook - how much Edith loved Gregson, loves Marigold, and is herself evolving into a modern businesswoman with the magazine just as Mary is with the estate.
We don't know which one says something which makes everyone gasp during the cat fight, but if it's Mary I would hope it would make the others in the family take action and scold Mary more effectively. They actually do have a lot in common, though Mary would deny it at first. Maybe that's why Mary does not like Edith - she sees the dark reflection of herself. Either way, she needs to be the one asking Edith for forgiveness.
As for someone dying if it must comes to that, my votes are Violet and Rosamund. I know for some it would be treason because the Dowager is a great character with great lines, but it's not because of her age. This goes back to the family not caring for Edith's heart. Violet's and Rosamund's not caring is what drove Edith to run away to keep her daughter. Perhaps Rosamund would be the first option, if Edith moves to London with Marigold and would be the one to stay with if anyone else goes to London.