All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
According to the correct opinion of the scholars a person is obliged to perform ‘Umrah only once in his lifetime. Therefore, if your wife is able to perform ‘Umrah, then she is obliged to do so. As far as you are concerned, you are not religiously obliged to take your wife to perform ‘Umrah and you are not obliged to accompany her, but you are obliged to obey your parents within what is permissible [if they do not order you to disobey Allaah]. Their objection to you to accompany her is not an act of disobedience; rather, it is only disliked for them to do so because it seems that they do not have a sound reason for objecting to you doing so.
Therefore, it is better not to disobey them, but you should try to convince them that they will be rewarded if they give you permission to go with her and that they should not religiously prevent you just because your brother and his wife did not perform ‘Umrah before, and that this is ignorance of the religion.
Afterwards, if they give you permission, then this is what is required, otherwise it may be that it would be better for you not to disobey them. However, if you act contrarily to their instruction because they do not have a sound reason for preventing you, then we hope that you are not sinful because some scholars permitted acting contrarily to one’s parents in such a case, and they said that if the parents order their son to do something or object to him doing something out of foolishness, then their attitude is not considered and it is not an obligation to obey them; for more benefit, please refer to Fatwa 84942.
As regards you wife, if the distance between Makkah and your place of residence is a travelling distance and she does not find a Mahram to accompany her, then she is not obliged to perform ‘Umrah as she is not able to do so. However, if your wife finds a Mahram or that the distance is not a travelling distance, then she may go even alone if the road is safe.
Finally, if should be noted that if your parents prevent you because of believing that it is forbidden for you to perform ‘Umrah before your brother and his wife go for ‘Umrah, then this is a religious innovation and this is forbidding something which Allaah made lawful. In which case, they are obliged to repent to Allaah.
Allaah Knows best.