I think you are correct that LM could make the ladies at the cottage sociality uncomfortable if she chose and I agree she shows no propensity (taste) to be resentful or act meanly towards them. :D

]Having just experienced a wife's influence on her husband, which caused suffering, I feel sure they would wonder about this wife's influence on hers.

In this just a general statement on Fanny’s meanness making them suffer or are you saying her interference in Chapter 2 caused the Dashwood ladies to suffer and inturn they are automatically suspicious of Lady Middleton’s character before they meet or even hear anything about her? I would agree Fanny’s interference in Chapter 2 does cause suffering for the Dashwood ladies but I do not think they knew Fanny talked their brother out of helping them with money. Other Fanny attacks are on the record so to speak: They all know of Fanny’s distain for an attachment between Elinor and Edward—Fanny make’s terrible insinuations to Mrs. Dashwood, Elinor is smart enough to figure it out for herself and Elinor tells Marianne in Chapter 4.

Her eagerness to be gone from Norland was preserved from diminution by the evident satisfaction of her daughter-in-law in the prospect of her removal; a satisfaction which was but feebly attempted to be concealed under a cold invitation to her to defer her departure. (Chapter 5)

Mrs. Dashwood certainly knows Fanny is happy when they prepare to leave Norland and I suspect her daughters know too but I could not find a reference from their point of view. On Fanny’s specific interference in Chapter 2 however I think all three are unaware.

In a very few weeks from the day which brought Sir John Middleton's first letter to Norland, everything was so far settled in their future abode as to enable Mrs. Dashwood and her daughters to begin their journey. (Chapter 5)

Mrs. Dashwood had confidence in John honoring his father’s request up into the last weeks of their stay—Chapter 5 and I do not think she would have had continued confidence in him if she had known of Fanny’s interference. Fanny does The Deed (Chapter 2) before Mrs. Dashwood receives the letter from Sir John (Chapter 4) and Mrs. Dashwood continues to believe John will honor his promise for several weeks after that—Chapter 5:

Now was the time when her son-in-law's promise to his father might with particular propriety be fulfilled...But Mrs. Dashwood began shortly to give over every hope of the kind... (Chapter 5)