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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Udh-hiyah is a confirmed act of Sunnah for your mother as long as she owns money from which she can slaughter an Udh-hiyah. However, it is not permissible for you to buy an Udh-hiyah except with her permission. If she permitted you to buy it, it would be permissible for you to buy one and slaughter it on her behalf. It does not matter if any of your brothers dislikes that as long as your mother is sane and not declared legally incompetent. Furthermore, making Udh-hiyah will not harm her; rather, she is direly in need of reward from Allaah The Almighty particularly at this age in which we wish her a good end. Try your best to advise your brothers, and those who do not perform prayers in particular, and remind them of Allaah The Almighty. Be united on doing what is best for your mother according to what pleases Allaah The Almighty and give precedence to her interests in the Hereafter over everything. Do your best to let your mother gain reward from every possible means, and we ask Allaah to Grant her and us a good end in this life.
You are not allowed to slaughter an Udh-hiyah on behalf of your father from your mother's money except with her consent on the condition mentioned above, namely, the soundness of her mind.
Allaah Knows best.