The ring travels on the goat's belt (thankfully not through the goat's bowels which could have been a stinker!) and returns to Arnav who uses it to extract an apology from Khushi. Our self-respecting miss, however, refused to give in and asked him to keep it, showing just how much importance she gave it. If Khushi's bua had not intervened in the opportune time and emotionally blackmailed her into getting it back, it would have been thrown away by the angry man. Luckily it got a second lease of life as poor Khushi, with all her khushi wiped out of her face, pleads with Arnav to return it to her. Moved by her tears he hands it over to her. When he sees her struggling to put it on her wounded finger, he tries to help her slip the ring in only to find her snatch her finger back and drop the bombshell that it was her engagement ring. The guy may have well been electrocuted hearing these words and the ill fated ring gets dropped once again and rolls to the feet of the wrong man's wife who finally puts it on Khushi's finger.
So finally the ring has reached the right finger after a lot of drama but the purpose for which it was originally meant was defeated. If anything, it made sure that the right man knows of its existence so that he can nip any prospect of a follow-up wedding of Khushi with the wrong man. Now will the right man take the right decision or hasten towards another wrong decision?
By the way, Anjali slipping the ring on Khushi's finger seemed to indicate to me that this ring has established a bond between Anjali and Khushi and not between Shyam and Khushi. So when the troubled times arrive, Khushi will willingly accept any hardship for the sake of Anjali's happiness. Going by Buaji's words, the vein in the left finger connects to the heart and hence by putting the ring on that finger Anjali has established that bond with Khushi's heart. Since Arnav has already put the bandage ring on that finger, now both the siblings have bonded with Khushi.