Within the {M} ain {V} erse; Eris is not the biological mother of Alkeme, Aethon, Archelaos and Atreus. Instead, she is a Mother Figure. Even though they aren't her blood, Eris loves them and treats them as her own. Though, it is often said that she favors Archelaos and Alkeme out of all of the children. Eris doesn't admit to any favoritism. She does admit to having a dislike for Hades, however.
Within the {A} lternate {V} erse in which Alkeme is Loki's daughter; Eris is her biological mother. Eris is not fond of any Gods within Asgard due to their treatment of her beloved Trickster as well as her daughter. Eris is known for having quite the temper in regards to what happens to either of them.