Is a vow made conditional on giving birth to a child valid? Is it permissible to give money designated for 'Umrah to one's sister or her husband if they refuse to perform it? And is it obligatory to perform 'Umrah for the two other sisters to avoid family problems?

The vow must be fulfilled when its condition is met, because a vow is a grave matter in Islamic law, and Allah and His Messenger have made its fulfillment obligatory. It is not permissible to change the vow or abandon it, but you should maintain kinship ties to the best of your ability.