Theory: The fall of the Dreemurrs
Well, it all started with the Dess incident, right? Asgore focused on the case and ended up being fired for a reason we still don't know.
In short, I believe the obsession with solving Dess's case is what caused the family's separation. I say this because in the "Earthbound: Halloween Hack" (made by Toby) a similar, though different, situation occurs with Dr. Andonuts's family:
I think Asgore was so absorbed and focused on the Dess's case that he neglected his family.
He wasn't there when they needed him most, and Toriel had to handle everything on her own. This left Toriel feeling vulnerable, helpless, stressed, and frustrated as she tried to care for the children who were suffering from the trauma. This triggered the arguments and the impending separation.
Surprisingly, Spamton delves deeper into this topic in the "Undertale 10th Anniversary" stream. To be more precise, from this point onward:
Now I'm going to show you how I interpreted what he said:
Spamton <( What do you think of Asgore? Of course, Asgore is cool.
He wears (???) every day, and by that I mean he tries really hard in the (???) every day.
One day, he went to his house like every day and begged Toriel to let him be in it. Of couse, she shut the door in his face, even though it was his house, but the next day, she woke up and saw him still waiting there. She shut the door again, even though it was still his house.
Seeing his dedication, he decided to bother everyone every day. It's, uh, still a work in progress.
Anyway, ha ha. Poor guy, huh? That Asgore...
He could really use a little... of money.
It seems Tenna wasn't the only witness. Spamton saw how Toriel take Asgore out of the house.
Spamton <( Have you ever heard of a talking flower? Right kid, flowers talk.
Good job donating that money to a good cause, but this holiday season, shouldn't you help the ones in the most need...? That means Asgore.
So, in this holiday season, I'm asking you my esteemed customer, that all the salty stuff I'll take for me, please, can you foot the bill? Otherwhise, I may fit my foot in your ass if you @#$% this. After all, I've sustained extreme personal damage due to a certain idiot TV.
Okay, in my understanding: Spamton speaks in a broken way, he wants us to help Asgore, and it seems that signing the deal with Tenna brought him problems that led to his downfall.
Perhaps Tenna, in his naiveté, thought Spamton would accept the deal to achieve greatness together, hoping to draw the Dreemurrs' attention so they would reunite and forget their troubles with them, but it failed miserably.
I could be wrong, though, you'll see how to interpret this part. Spamton is sometimes difficult to understand.
As for Asriel, we know he gets very bad when he loses someone, so I think Dess's disappearance left him deeply depressed. However, seeing how the situation was developing in his family, he decided to focus on his studies and remain stable for Kris, since they needed him.
He hid his pain with a smile, repressed it, tried to move on, be a good brother to Kris and go out with other girls to fill the void left by Dess, but things kept getting harder and harder and he felt numb, empty inside.
The fact that he's at college right now may be giving him some space and time to reflect and process things better.
Perhaps he's going through the same process as "Hero" from "Omori", but we won't know until he appears.
Now, with Kris, it can be said they were the ones who had the worst part.
It's unknown what happened between them, Dess and the Shelter, but it can be said it was something bad, it caused a domino effect and Kris blames themselves for everything.
"It's my fault Dess disappeared."
"It's my fault the Holidays aren't okay."
"It's my fault Noelle is suffering."
"It's my fault my parents are fighting."
"It's my fault Asriel left."
"It's my fault nobody loves me."
"If I had done this, none of this would have happened."
"Why wasn't I born a monster?"
"Damn it! I hate myself!"
Because of all this, they began to distance themselves from everyone, even their loved ones, for fear of continuing causing trouble and keep hurting others. That's why they stopped being who they were and became the broken person we met at the beginning of Deltarune.
Toriel probably took them to therapy because she wanted to know what was wrong, but Kris repressed the memory because of the trauma, and even if they said something, probably no one would believe them. The monsters would treat them like a crazy person, just like their dad.
Perhaps it was then, in their vulnerability, they joined Carol and the Knight. To try to solve everything and see how to deal with the prophecy later, although currently they seem to have doubts about whether or not to continue with the job. We also don't know if they're being threatened if they fail or not, so they're in a complicated situation.
In my opinion, in this family there are neither good nor bad, just people who made some mistakes and are paying for them.
They're not that different from their counterparts in Undertale, and I don't think they'll ever be the family they once were. However, we'll have to see how things unfold in Chapter 5 and if we can at least get them to talk or make peace with each other.