In Undertale it makes sense why she left him, Asgore was killing innocent human children, he killed six children, not only that he didn't even need to kill that many children, as Toriel points out he could have gotten one human soul, walk outside the barrier, then outside the barrier just find humans that where already going to die and free all the monsters, but he didn't commit and was basically killing innocent children. In Delta Rune all we know is that he used to be chief of police, then something happen and he was fired, and Toriel left him. Whatever he did Kris is still kind of pissed, but he still loves Asgore as if you bring an egg to the flower shop and interact with the fridge, Kris will put the egg on the fridge for Asgore to eat.

Whatever happened, I hope we'll get to fix it. Asgore deserves happiness too. He's not just a running joke.