How can one deal with a harsh, domineering mother, and what is the effect of this on performing the Hajj pilgrimage, especially with the children's efforts to honor her and their endurance of her hurtful actions?

You are not permitted to incite your mother against your wife to harm her. Strive to treat your mother well and improve your relationship with her, and do not sever ties with her. If she insists on her stance, you bear no sin for estrangement or severance, and this will not affect your Hajj. Strive to supplicate for her guidance, and try to mediate through those who have a good relationship with her to resolve the problem.