You make a good observation that Mary writes as though she and Fanny were a team against Maria and Julia, etc.. This is something Mary may have been used to all her life. Living with her aunt and uncle, she and her aunt would have made a team, and her uncle with Henry, another.

I think this goes with Mary's competitive nature, and may be natural in the London crowd she is used to being with. I have three very particular friends who have been all dying for him in their turn; and the pains which they, their mothers (very clever women), as well as my dear aunt and myself, have taken to reason, coax, or trick him into marrying, is inconceivable! Chap. 4

In another way, she and her brother are a team. He confides to her his schemes of feminine conquests, and she protects and helps him along the way. Mary quite possibly has been playing both teams- trying to trick Henry into marriage while helping him in some insidious scheme at the same time.