Having abandoned (or at least heavily revised) her principles to align more with her father's, Barbara has apparently regressed to being about five years old, clinging to her mother's skirts and begging for help in picking out a house for her and Dolly to live in together. Lady Brit seems more than a little disgusted by her daughter's behavior:
LADY BRITOMART [coming from the shed and stopping on the steps, obstructing Sarah, who follows with Lomax. Barbara clutches like a baby at her mother's skirt]: Barbara: when will you learn to be independent and to act and think for yourself? I know as well as possible what that cry of 'Mamma, Mamma,' means. Always running to me!
SARAH [touching Lady Britomart's ribs with her finger tips and imitating a bicycle horn]: Pip! pip!
LADY BRITOMART [highly indignant]: How dare you say Pip! pip! to me, Sarah? You are both very naughty children. What do you want, Barbara?
BARBARA. I want a house in the village to live in with Dolly. [Dragging at the skirt] Come and tell me which one to take. (3.429-432)
It's hard to see the once very commanding "Major" reduced to this childlike behavior. Perhaps the message is that Barbara is ultimately more of a follower than a leader—and now that Undershaft's ideas regarding power and wealth are holding sway, her true nature is revealed? Or maybe she's just placating her mother and making her feel like she's still needed after the ego bashing Lady B got in Act III? It's kind of hard to tell what's going on with this sudden baby-like behavior . . .
In any case, Undershaft's views have been almost universally adopted among the family, which means that proper order and moral sense are in place…and by choosing a house near the works, Barbara is indicating she's all in.