How can the dispute between siblings be resolved regarding the estimation of the additional share that the father promised to give to the sister's husband in exchange for his purchase of land shares, and must the sister's husband fulfill his promise to him in this regard?

If your father agreed with your sister's husband that for every share he buys and registers in your father's name, he will give it to him in addition to another share in exchange for his efforts, then this agreement must be fulfilled. If the sister's husband claims that he takes one and a half meters for every meter after segregation and has no evidence, and you claim otherwise, then judicial custom dictates: "The burden of proof is on the claimant, and the oath is on the defendant." If you are unable to swear against his claim, then you must either give him what he claimed, or reconcile with him for something that satisfies both parties, while taking into account the kinship and the effort exerted by your sister's husband.