Is it permissible to include one's wife and the deceased in the Udhiyah (sacrifice), and who refrains from the prohibitions if the wife is included? And is it permissible for the husband to be a partner in his wife's Udhiyah in which she includes her deceased parents?

It is permissible for a husband to include his wife in his sacrifice (Udhiyah). In this case, the wife is not required to refrain from cutting her hair, nails, or skin, because the one obligated to do so is the sacrificer himself. However, if the wife is the one making the sacrifice, or if she is a co-participant in a sacrifice where partnership is permissible (such as camels and cattle), then she must refrain from cutting her hair, nails, or skin, just like the sacrificer.