Yes, as said above, Tom and Violet did discuss the fact that Edith wasn't there. So it may have been a question of doing what she could do at that point. I also think it's the practicality of it.
Firstly, you can't fix Bertie and Edith instantly, whether we like it or not. This is because, for Bertie, it is a breach of trust that has lasted their entire relationship, and he will need time to absorb, reflect, put everytihng into perspective and examine whether that has affected his feelings. The cliche that "time heals all wounds," may actually be very pertinent here. With Mary, it's a pretty quick fix because it's not a breach of trust at the core of her relationship, it's just coaxing Mary out of her icey-fortress of a heart and telling her to be honest with herself, if she's fallen in love then just go for it. Violet is a wise lady so I trust she knows all this.
Secondly, Bertie is the one stopping the relationship, not Edith. Violet, by going to Edith, has no effect on getting Bertie to come back to Edith. She can be comforting, but she realised she could not do that from York when Edith turned out to be in London. Violet would have to go to Bertie and I'm sure she doesn't want to do that without figuring out where Edith is at yet. Mary was the one in the way of her own happiness with Henry, Violet knew she could talk Mary round.
Thirdly, Violet knows Edith and Mary are different and that Mary can be won round by talking to her. Edith tends to deal with heartbreak and anguish alone. You may say that is because she is abandoned, but no, she does choose: she was going to the abortion "clinic" alone (but Rosamund turned up), she ran to London with Marigold without telling anyone, and after Bertie broke up with her she went to London (even though Tom offered to help). I think the vastness of London suits her. She once said that no one cares much about how people live their lives, I think she likes that she's free and not under a microscope so much there. The way to bring Edith back to Bertie is not really by talking to her, but by bringing her out of her solitude and orchestrating a meeting is probably the best way (as we see in the CS trailer)
Mary, on the other hand, has always been lifted through pep talks whether by her mother, Carson, Violet, Tom etc. In S6E 7, Tom tried to after she broke up with Henry and I think that was when her heart had shut down completely - ultra-Violet can get through though, because she's amazing.
Fourth, I would want to sort Mary out first anyway. Shame her about how she treated Edith so that she doesn't do it again. It would be really unhelpful if Violet got Edith and Bertie back together somehow, and Mary was still being a sour puss, sulking and being destructive - it may come in the way of an already difficult reconcilliation. So for practical reasons, remove the obstacle (Mary) for Edith, and smooth the path for Bertie to come back.
Lastly, Violet's quite old now so she doesn't have time to run around England. She already returned speedily from France so I think she'd much rather deal with Mary first as she is there.
Sorry that was long, but I'm a major defender of the Crawley Family and I believe they love Edith. I just wanted to argue that they're not just abandoning her, or favouring Mary.