I have strongly disliked Garima in the past and I felt she never acknowledged Khushi's contribution to the family and never appreciated her hard work. I was fuming when she slapped Khushi.
But today I felt, she was absolutely right and she acted logically and rationally.
As for her behavior towards Arnav, he is her son in law so she is treating him with love and respect. He is also a guest at their house. The show strongly focuses on things like sanksar and culture. Treating a son-in-law and a guest is a part of sanskar and good manners. It has nothing to do with where a person lives or comes from. It's something any mother would do, anywhere.
She is also thinking about Khushi's well being here. Her daughter had a runaway love marriage ( that's what the families think ) and she is going to live with this man for the rest of her life. If her husband is not treated well by them, her daughter's in laws may feel offended. Her daughter who loves this man (from her POV), may also feel offended if her hubby isn't treated with respect.
As for scolding Khushi today, she was right. Khushi kept insisting that he calls Garima, Amma. But he was clearly uncomfortable and Garima noticed it. Her repeated insistence was making things awkward between Garima and Arnav.
When Arnav screamed that his mother is dead, Garima being a mother, who once adopted her orphaned niece, understood his pain of loss. She realized that respect doesn't come from how you address a person. It comes from within.
From Khushi POV, she was pestering Arnav (consciously) to annoy her. Subconsciously, maybe she was just wishing for him to accept her family as his own the way she has accepted his family.
Was Khushi wrong to insist ? If she can address her aunt as Amma, why can't Arnav? If Arnav is an orphan, she is an orphan too. Then what's the problem?
When Khushi lost her parents, she was only eight and she didn't even understand what dying actually meant. While Arnav was much older when his parents died and they also died an unnatural death. We know from the flashbacks that his mom was maybe killed or committed suicide.
Garima and Shashi are Khushi's aunt and uncle. so it's obvious that Khushi grew up calling them Masi and Mausaji.
Who Knows, when Khushi was adopted, may be she also had difficulty addressing Garima as Amma. After all Garima is her aunt and she probably called Shashi-Garima as Masi and Mausaji even after she was adopted. Maybe she started calling her Amma much later.
Garima may have a preference for Payal for some odd reason. She may be biased at times but she is also the lady who embraced her orphaned niece when she was all alone.