The problem is that in a lot of ways Mary didnt matured with the time, agree that Edith caused a lot of problems but who doesnt. But Mary in her 35´s still behaved like a 15 year old teenager and not like a woman as she should be; for example look how she based her relations with men, basically only playing power games with them and with Henry Talbot in particular. The war and knowing other people caused a great impact in Sybil and Edith but not in Mary, because in that period she was too absorved dealing with Matthew, in other words, her problems.
I think that the main reason behind that behaviour is that being always the favourite of her parents in the end delayed Mary´s development, besides nobody in the family besides Matthew (and in a little way), Edith and in the end Tom, pointed to her that she has flaws.
In conclusion Mary is a very sensible person, she acts as she didnt care, but she cares deeply the opinion of others about her, notice how she drop a tear when she knew that Gillingham was engaged again, and then when Mabel Lane Fox invited to her wedding, or that Tom was leaving to America. All that because she was a woman who canot deal with failure or when things dont go in their way, and that show us a very sensible but also inmature person.
I think that very deeply she is scared of people who knows "the real Mary" and among them is Edith; when they yelled each other Mary was incapable of saying anything and also when Edith came back before the wedding.
The cause of all those problem is to me the way that both of their parents raised them, especially Cora, to the very end Cora was using the same condescenting tone towards Edith. At least Robert tries to understand both of her daughters, but Cora dont do anything in that way.