Both Uses of

dispute
in
Sense and Sensibility

But I was willing to shew you that I had not forgot our old disputes.†
Chpt 17 *

disputes = disagreements, arguments, or conflicts

No one could dispute her right to come; the house was her husband's from the moment of his father's decease; but the indelicacy of her conduct was so much the greater, and to a woman in Mrs. Dashwood's situation, with only common feelings, must have been highly unpleasing;—but in HER mind there was a sense of honor so keen, a generosity so romantic, that any offence of the kind, by whomsoever given or received, was to her a source of immoveable disgust.†
Chpt 1

Definitions:

(1) (dispute as in: their border dispute)
disagreement, argument, or conflict
(2) (dispute as in: She disputes his claim.)
challenge, argue about, or fight over