Is the questioner sinful for shunning her sister, who is demanding 40,0 Riyals for a check that was a guarantee for an inheritance the questioner did not receive and relinquished to her brother, while the questioner offered 10,0 Riyals?

It is not permissible to abandon your sister due to a financial problem. The duty is to maintain ties with her, even if she does not desire it, and this connection should be maintained in the customary way in your country. You must repent to Allah for severing ties with your sister and strive to reconcile with her, for this world is fleeting and should not be a cause for estrangement between siblings.