Is it obligatory to pay for the marriage expenses of a sister whom the father refused to provide for before his death, out of the inheritance before its distribution, in order to achieve fairness in the gift among the children?

You are not obliged to pay for your sister's wedding expenses from the inheritance before its division. It appears that the father spent on your marriages due to your need, not as a preference, and there is no harm in this, even according to the Hanbalis who mandate equality in gifts. It is permissible to favor some children with a gift due to need or merit, or to withhold it from others due to their wrongdoing or innovation. If you give her the money as a donation, that is better.