Will we be rewarded for the Udhiyah (sacrifice) if the husband's brother pays our share in it while we are financially capable of paying, or is the reward contingent upon returning the money to him?

It is not permissible to share in the price of an sacrificial sheep (shah) if it is for Udhiyah (sacrifice), and this is a matter of consensus among scholars. However, if it is a camel (badanah) or a cow (baqarah), then sharing in its price is permissible according to the majority of scholars. They substantiated this with the hadith of Jabir (may Allah be pleased with him): "We slaughtered with the Messenger of Allah (peace and blessings of Allah be upon him) in the year of Hudaybiyah, a camel for seven and a cow for seven." As for the Maliki school, they held the view that it is not permissible to share in a camel or a cow, but the preponderant opinion is that of the majority of scholars.

As for including others in the intention of the sacrifice with a sheep without them contributing financially, this is permissible. This is supported by the hadith of Abu Ayyub al-Ansari: "A man used to sacrifice a sheep on behalf of himself and his household." Likewise, the Prophet (peace and blessings of Allah be upon him) sacrificed a ram on behalf of himself and those among his Ummah who did not sacrifice.