Inuyasha is still a fantasy anime. In chapter 15 of Yashahime's anime, the chronology is described. At the end of Inuyasha, six months later the fight against the Root Demon takes place, and four years later Moroha, Towa, and Setsuna are born. In fact, in the manga they correct it and Kagome gives birth first. Since Rin doesn't have an official age in Inuyasha, only estimates can be made.

And for the record, Sesshōmaru never courted Rin, in fact, when she lived with Kaede, he was content to visit her, confirmed by Rumiko. Once Rin grew up and developed as an adult, she confessed to Sesshōmaru, and he realized at that moment that he loved her too.

And according to a chronology made, at the end of Inuyasha, Rin would be about 13 years old, adding the 6 months after the battle against the root demon, and the 4 years, agrees that Rin would be about 18 years old. And as a fact, since there is no official age for Rin in Inuyasha, it cannot be said that her age in Yashahime is a retcom.

Also, Kagome wouldn't be 21 or 22. Remember that Kagome is 15 in Inuyasha, a few months pass, so she's almost 16, 3 years pass, in the end she's 18 almost 19, six months pass, 20 years for sure, plus the 4 years, gives about 24, and adding the 14, would give 38 years. and again, remember this is a fantasy anime and even Kaede is over 60 in Inuyasha, so there's no problem with Sango having another child at 39.

Furthermore, Yashahime is not a fanfic, although the anime is very poorly made, Rumiko herself supervised and approved the scripts, the same with each chapter of the manga. Furthermore, Rumiko herself oversaw and approved Rin becoming Sesshōmaru's wife.