Credit goes to Maham(Allbut1) for this beautiful Banner
In many ways I think it goes back to that ever-relevant statement of the Mittals, that the biggest enemy of this relationship is Yash and Aarti's memories. To see that come true in a different light every so often in the course of the story is a reiteration of the theme they have started with. These are two individuals that have similar sensibilities and outlooks on life, that are totally compatible on a practical level, even if you don't want to consider all the signs of divine ordinance and kindred souls. And yet they both bring so much into this relationship that constantly prevents them from discovering how alike they really are and how successfully they could co-habit (for now), if they only allowed each other.
At first it was clear that Aarti did not trust Ansh with anyone. She didn't mind others caring for him physically but somehow she had to be the medium through which he saw the world because she believed that nobody else could stand by him and keep the faith the way she would. Prashant's absence as Ansh's father left a hole which Aarti refused to acknowledge and tried desperately to fill herself. But the day Yash took a bullet for her son, she realised there was someone else whom she could trust to keep Ansh's faith, who could make mistakes but who would ultimately never fail him. And that is when she accepted Ansh as Yash's father, when she knew he would do as much as she would for their child.
Yash is in an even worse position because unlike Aarti, he does not even trust himself with his children because the way he sees it, he can never be as good as Arpita was with them. Aarti at least has the agency to be an active parent because she trusts herself as one. Yash is maddeningly passive because even he is he is still so reliant on Arpita, who is not really there. The way he sees it, his kids are always going to be settling for second best, as his he. Life without Arpita will always be second best.
His problem here, and one that Aarti also has, since both of them have had traumatic events punctuate their lives, is that they believe the phases of life to be separate from one another. Aarti thinks she can close the door on her past and Yash constantly compares his past with his present, and finds the present lacking when he does. Both of them need to see that life is a continuum, their past was bringing to their present, and so it is never gone from us. Aarti must stop denying Prashant and Yash must stop fearing that he will forget Arpita. Their pasts will always be a part of them and they must accept that in order to move on.
Finally, from a parental perspective, Ansh is much quicker to embrace his new father because Yash is essentially filling an empty space, with all the information, though there wasn't much. The only information he got or needed was that Ansh used to write letters to his old father. Seeing as Prashant was never a presence in Ansh's life, and made it clear that he did not want Ansh, Aarti made the commitment to make Yash Ansh's father at all costs which is why she put in so much effort. On the other hand, Aarti is not at all filling an empty space but large shoes, that incidentally, nobody wants her to wear.
In Yash's eyes, Palak and Payal already had the perfect mother so I think even he is unsure of what he expects of Aarti. He likes the idea of her taking care of their physical needs but I think he is very much still possessive of his Arpita space with them on an emotional level and Palak is also very dependent on this space. From the sound of it, she was the most shocked and affected by Arpita's death and after all this time she has found a precarious balance. Aarti's entry into their world has tipped the balance and she feels a lot of frustration, with nobody to take it out on and nobody to understand what she is going through.
Yash and Palak could be instrumental to each other's healing because they are so similar in nature and are going through much the same pain, fearing forgetting Arpita, whom they so loved and who loved them. For both of them it sounds like she was the only one who made them feel safe and understood and they feel fierce loyalty and intense guilt when they are reminded of her, because being reminded means you forgot in the first place.
They are bound by grief, yes, but not by healing. And until their relationship evolves, Aarti cannot be a part of their family because she cannot share in their grief. So at this point, really the only way left to her to break into their "Arpita club" is to somehow identify with Arpita herself. She has to somehow affirm that by accepting her they are not forgetting Arpita and convoluted as it sounds, maybe the only way to do this is to remind them of Arpita when they are with her. That way Palak will unconsciously bond with Aarti guiltless because she is remembering her mother at the same time. And by the time Aarti sheds her Arpita-avatar, Palak will be happily attached to Aarti herself. Or so we hope...