Another idea: Marianne's dislike for Fanny was equal and opposite to her love for Norland, thus making her reaction to the scheme neutral. I am only half-joking.

I think Mrs Dashwood here behaves like a good parent, and her relationship with the girls appears in a very positive light. She made the decision on her own, but didn't implement it without discussing it with her daughters first. Although it's ultimately her decision to make, she cares about their opinions and feelings, and recognizes they have a say over the decision. They must also have discussed about moving out prior to the arrival of the letter, so Mrs Dashwood probably knew the girls' views when she wrote the reply. Elinor wished for affordable rent and some distance from Norland, and Marianne probably just sort of dismally accepted that they would have to leave eventually. It was reasonable to suppose they'd either agree or at least submit to the inevitable.

Yes, Elinor does seem to influence her mother heavily in practical matters. In chapter five, "[Elinor's] wisdom limited the number of their servants to three" and Mrs Dashwood "agreed to sell [the carriage] likewise at the earnest advice of her eldest daughter." In chapter one, she is introduced as the eldest daughter who posessed "a strength of understanding, and coolness of judgment, which qualified her, though only nineteen, to be the counsellor of her mother, and enabled her frequently to counteract, to the advantage of them all, that eagerness of mind in Mrs. Dashwood which must generally have led to imprudence. "

I agree that Mrs Dashwood mostly seems guided by Elinor's prudence in practical matters, but it doesn't neccessarily follow that she heeds Elinor's advice in general. Maybe practical matters are just Elinor's territory. Mrs Dashwood just doesn't strike me as the type to exercise strong authority over the issue of buying new furniture or whatever. She probably makes enthusiastic suggestions of various degrees of outrageousness, and then Elinor decides which, if any, can be implemented.