Is it permissible for a woman, Islamically, to confine herself to her role as a mother to her children without marital relations, especially if the husband agrees to this proposal, and she desires to avoid divorce for the sake of the children, particularly given the husband's neglect, travel, and leaving her with her children?

A husband's neglect of one of his wives is forbidden (haram), and he will come on the Day of Judgment with his side ﷺ skewed. A wife should not seek divorce because her husband married another, unless this is accompanied by clear harm that cannot be removed. It is permissible for a wife to remain married to her husband and waive some of her rights by mutual agreement, as stated in the verse: ﴿And if a woman fears from her husband high-handedness or estrangement, there is no blame upon them if they make terms of settlement between themselves.﴾ [An-Nisa: 128].