What is the Shar'i (Islamic legal) ruling regarding ostracizing a sister, insulting her, verbally abusing her, and slandering her due to a dispute between them over the sale and purchase of a share in a house, knowing that the sister claims she was forced into the purchase and was unable to pay the agreed-upon amount because she was asked for additional sums? And is the purchasing sister sinful or at fault for this purchase?

If the situation is as you described, then you did not err in purchasing your sister's share, and you are not obligated to expedite any portion of the payment beyond what was agreed upon. What your sister did—slandering you, boycotting you, and her son cursing you—is a clear injustice and a great transgression, because severing ties of kinship is among the major sins. Nevertheless, this should not lead you to sever ties with your kin. "The one who maintains ties is not the one who reciprocates, but the one who maintains ties is he who, when his kinship is severed, connects it." If you are as you described yourself, then "it is as if you are feeding them hot ashes, and you will continue to have a supporter from Allah against them as long as you remain steadfast in that."