I don't know how many times I've read in the fandom the interpretation that "Kagome is Kikyo in another life where she can be a normal woman and be with Inuyasha." I had already made a post with information from the manga wideban version where Rumiko explaining that Kikyo's "other life" occurred when she was resurrected in a clay body and NOT as Kagome and now I’m going to use information from the regular manga and the profile book as well.
In the manga chapter about Kikyo's resurrection, Kikyo herself runs away because she doesn't want Kagome to take back the soul still remaining within her and the reason is that if those souls returned to Kagome's body it would mean Kikyo's death, as she would no longer be herself. Kikyo refuses to die and decides to remain "alive" within the clay body. That is the point Rumiko refers to in the wideban version of the manga: Kikyo living her second life in the clay body and she developed her character until she dies for the last time saying that she could finally be a normal woman her soul rested in peace.
The profile book also makes it clear that Kikyo is a dead person and that the only way for her to be with Inuyasha was for both of them to die together, which is why she tried to drag Inuyasha down to hell with her. It also explains that Kikyo envies Kagome's life and even tried to attack her.
In conclusion: Kagome was NOT written to be Kikyo's "other life" and neither "her second chance to be with Inuyasha." Rumiko wrote the exact opposite of that. Therefore, this interpretation is incorrect, and as a Kagome fan, I find it frustrating that people in the fandom can't separate Kagome from Kikyo and Kikyo fans even use her as a consolation for their fav character's death and their failed ship with Inuyasha.