Thank you for the translation and all the hard work! Great work as always!!
Now I'm wondering they've split up, not because of anything emotional between them but due to circumstances. Like something happened to the previous mother and Momoko, who is her daughter was supposedly to take over after her, but refused to because she loved to dance, but if she takes over being Mother, she can't dance anymore. Also given that Momoko's traits, she wouldn't be a good Mother either. So I'm wondering the current mother, Chikako, knew that, took over for the sake of her friend and abandoning her role as a Geisha. And the reason, Momoko doesn't visit or contact her old house anymore because she knows the sacrifice Chikako made for her, and doesn't want to burden her anymore, and aims to be the best because she has to carry own two people's ambitions.
I may be cooking too long because this arc is longer then I expected and I can't help myself lol