"They are wanted in the farm much oftener than I can get them." [for the farm] (Since Mrs. Bennet presumably is always asking to use them for traveling purposes, etc.)

"But if you have got them to-day," said Elizabeth, "my mother's purpose will be answered." is more like your first sentence "if the farm has them today, my mother's plan must occur," The work answered is more like the word satisfied, rather than disappointed.