I actually agree with you. Even though Pakhi and Toshu are badtameez and talk in such a disgusting way I agree with the crux of their arguments.
Firstly, very easily Anu said to Pakhi that she is no longer welcome to his house. Even if Pakhi had talked this way to Baa-Bapuji this way in front of Vanraj would he have told her she is not allowed in his house? Because in this setting it is also Pakhi's house. So clearly, the freedom or right Pakhi has in Shah house she doesn't have in Kapadia house. Which is fine in itself. But Anupama and Anuj need to stop pretending that this is not true.
Secondly, who is Anuj to interfere between Anu and Pakhi? He is an outsider. Pakhi may or may not be interested in Adhik for his lifestyle. We can understand her POV because we see everything that is happening. But what would Anuj know about that? What right does he have, with his incomplete information, to accuse Pakhi of being a gold-digger?
The crux of the issue is choti Anu. Toshu and Pakhi cannot accept her as a sister. They lost their mother to another house and now have to share her with another child stays with her all the time. I know we all say that Pakhi Toshu and Samar are adults who don't need her, but we all know that unfortunately, children don't consider themselves to be separate entities from their parents. Here, if Anu's children should stop depending on her, she should stop expecting them to treat her with the same level of affection/love? Because the relationship they have shared thus far is not a healthy, independent relationship and both sets of individuals have clung to it.
Why does Anupama list out the number of things she has done for the family? When parents do things for their children, they should not use them against her in the future, in a separate argument. And Anu implied that when she did one thing for herself her children had an issue with it. She has been doing a lot of things for herself (marrying Anuj, adopting choti Anu) and that is great, because everyone should live for themselves, but that is not the issue her children have with her. She expects her children to accept her decisions whole-heartedly (by bringing choti Anu to the Shah house always and calling it their nanu-nani's house), without giving them the space to come to terms with it, if they ever do.
Disclaimer: Toshu and Pakhi are toxic AF but at their core, their arguments make some sense.