The sentence suggests that the woman cares more for her children than she does for her husband. Both options A) "a lot more" and B) "much more" convey the idea that her care for her children surpasses her care for her husband. However, "a lot more" emphasizes a greater degree of difference, while "much more" emphasizes the extent of the caring. So, both options are correct, but the choice between them depends on the emphasis the speaker wants to convey.
