I was brought up in a very similar environment as you which makes this extremely relate able! I grew up in the States as well but my mom has always been very, very conservative in her parenting (she became a lot more lenient as I started growing up), but those initial years of my childhood that I remember weren't exactly fun! In fact there are still times when I find myself thinking that the only thing I have learned from the way my mom raised me is how NOT to raise my own kids.
I honestly believe that kids react better to a situation when they are told why they have to do a certain thing rather than if you give them a because I said so response. And they're also a lot more perceptive than adults like to give them credit for, sometimes I feel that kids understand situations better than adults ever can and that's because they soak everything in and then come up with the simplest way to deal with it rather than run around in circles like I see so many adults do on a regular basis!
I feel that Payal and Palak are still young and can be molded under Aarti's love and care to become more open and social around others. They've always been put at such a high regard and are forced to follow so many rules and regulations that they find it difficult to just let go and have fun, mainly because they don't know how! And because they mainly stick with each other it becomes very difficult for them to share their stuff with anyone else. So just like Yash is going to become a positive force in Ansh's life, Aarti needs to slowly win the girls' hearts and trust because I have a feel that once they start trusting her that will pave it's way for a fierce attachment to her and that's exactly what we need this to build up towards!
At the end of the day though, it's only been a couple of days since the wedding, and all change and transition takes time to adjust to. Here two families are coming together to become one so obviously there will be conflict and friction as they try and find their place in each others' lives, but I am sure Friday's episode was just the beginning of better times to come. Aarti has already taken the initiative to become an active mother in PayPal's life and now Yash has done the same, so things will slowly but surely start getting better!