There is a ḥadīth in the Sahih of Bukhari which says that hajj has greater status than jihad. Does this ḥadīth not contradict all other hadiths on jihad? The Prophet (sws) put jihad third in good deeds after the salah (prayer) and serving parents.
I understand you refer to the following narrative:
حدثناعبدالرحمن بن المبارك حدثناخالد أخبرناحبيب بن أبي عمرةعن عائشة بنت طلحة عن عائشة أم المؤمنين رضي الله عنها أنها قالت يارسول الله نرى الجهاد أفضل العمل أفلا نجاهد قال لالكن أفضل الجهاد حج مبرور
Aaishah (rta) reported that once she asked the Prophet (sws), "We (women) consider Jihad the best of all (righteous) deeds. Shouldn't we (also) fight (in the way of God)?" He replied, "No, (you need not do that,) for the best form of Jihad (a woman does) is hajj-e-Mabroor.
We must not always disregard many important factors in our effort to understand the prophetic sayings. We know that every discourse certainly has a peculiar background. A questioner always asks something relevant to their circumstances. We can understand these things from the text itself. The question comes from the group of women, Aishah being their representative, because interpreting it otherwise would render it void of purpose. Muslims were not disallowed or restricted from participating in the wars rather they were obliged to do so. As an adult male Muslim, I cannot be expected to ask you, "Since Salah is the most rewarding deed should I offer it?" But a menstruating woman may reveal her concern on being stopped from worshipping God.
Another important thing is that the Prophet did not say, "Nay, Hajj is a religious obligation that is more stressed and is more rewarding." Rather he said, "the best form of Jihad is to offer hajj." He did not contradict the first part of Ayisha's (rta) statement rather he told her that, "yes it is, but your desire to participate in arm struggled does not suite you and is not required of all women."
Since Hajj journey through many of its rituals symbolically represents one's desire to die in the way of God therefore, it is a form of Hajj and women do participate in that. That is the best Jihad a woman is expected to do. They are not required to actively participate in wars.