I keep seeing arguments for both sides, so I'm curious what you think
I'm both seasons, the hotel crew doesn't go looking for Alastor (after the battle and during the kidnapping ). Most people say this is exactly what the crew should have done since Alastor doesn't care about them anyway and hasn't been helpful
Then on the other side, it's pointing out that charlie does still include him in her songs and drawings as part of the family . So it hurts when they leave him be
Where do you think Alastor stands in terms of the hotel family dynamic ?
I love Alastor being fully part of that found-family, whether he's shocked when he realizes he's been pulled into the family unit, or silently doing this thang and pretending he isn't in the family unit. I also love him yearning to be part of the group cuz he does want community and connection (Rosie described him as the "Toast of New Orleans" and we see him surrounded by a lot of people) and I like to think he wants that again, but he's very emotionally constipated, has trust issues, and doesn't want the vulnerability that comes from relying on other people.
I also love it when something happens to Alastor (or he leaves) and the Hazbin crew realize how integral he had become in their family unit.
But without my rose-tinted glasses, I think where Alastor stands in the family dynamic is that he's kind of just there. He joins them/watches their shenanigans, or lingers on the outskirt and observes everyone, but it's pretty easy to ignore for the most part; and I don't say that in the sense that they're disregarding him, but more like they've gotten so used to him lurking in the background that they don't question it or really notice it anymore. He's become another fixture in the periphery.
He joins them when he decides to, not when they request it--granted we haven't seen them actually invite him in their shenanigans (which is understandable, Alastor is an Overlord, he's dangerous, can be aloof and unsettling, and they may just not know how to interact with him, especially when his relationship with certain characters can be complicated, like with Husk (and maybe even Angel considering he and Husk are close and relate to each other due to their souls being owned by an Overlord and being at their beck and call). I can see Angel not really wanting to give Alastor that much grace due to his own experience with Valentino and how attached he is with Husk, even if a part of him may enjoy Alastor's company).
In the same vein, Angel's already shown that he's not that upset with Alastor leaving, see his comment when Alastor quit in "It's A Deal."
Angel: (laughs) You should've moved in sooner.
Which I also find interesting considering he and the most of the others looked happy when Alastor returned in season at the end of "The Show Must Go On."
So we've seen them be HAPPY with his presence but they also weren't that worried when he was captured by Vox nor did they make any move to go get him when he was being paraded around and humiliated, while also knowing how bad Vox is based on what Angel has said about him:
Angel Dust: Charlie, listen to me. I don't know what they promised you, but I'm telling you right now they are bad fucking news. Horrible fucking news!
Angel Dust: And I ain't being your little guinea pig. Especially in front of Vox. He gets off to watching people suffer. Dude is an absolute cunt-fuck.
Keeping in mind Angel's tone, he sounded genuinely scared and panicked. So they at least have a small idea of how bad Vox can be based on how closely Angel is associated with the Vee's. He literally knows them better than everyone else in the Hazbin crew, except for maybe Baxter (Alastor knows Vox very well, but that may not extend to Valentino or Velvette).
And yes, I know Alastor wanted to be where he was and he likely would've been annoyed if they did saved hi, but they didn't know that. They also may not be worried just because they assume Alastor can handle himself and as an Overlord he'll be fine.
Still, there wasn't a lot of concern for him or much of a negative reaction when he quit and left. Husk ended up leaving but he was using Alastor's absence as an excuse, and him leaving cause WAY bigger of a stir in the group.
Charlie had a moment of concern but she also seemed pretty annoyed that he was kidnapped:
Charlie: Ugh! This would just be so much easier with Alastor. He was supposed to host the hotel, not get fucking kidnapped and-- (worried) Oh, God, what do you think they're doing to him, Vaggie?
Vaggie: I'm sure he's okay. You know Al, he's always up to something.
(Which buys into them not being overly concerned because they're aware he typically has something up his sleeves). So there was a moment of concern but they moved past it pretty quickly.
I guess overall, Alastor's dynamic in the group is that he's not that involved in the family unit and not much changes in the group dynamic if he's not there. There's not a lot of concern put towards his absence (which we also see during the season 1 finale song--although keeping in mind that song was speed-running through an entire month so for all we know they had talked or expressed concern for him disappearing after the fight); and outwardly Alastor doesn't seem all that upset about it either.
Personally, I hope he gets closer to the Hazbin crew and becomes more integral in their found family. Niffty's the one who's shown the most concern for Alastor and genuine care for him seeing how she raced to his aid the moment she saw he was fighting the Vee's. I also think there's hints of Husk have a deeper, more complicated relationship with Alastor considering how comfortable he was about confronting Alastor about Mimzy, his confidence in Alastor protecting them/having their backs if Vox tried anything at the hotel, the fact that he showed up in the slot-machines during "Love In A Bottle" alongside Angel and Charlie, and his general apathy towards Alastor's presence whenever he's around.
I think those two (and Charlie a bit) have the closest relationship to Alastor out of the Hazbin crew, which I also find interesting since he owns the souls of 2 people out of those 3, but overall his presence isn't really needed nor are his absences really acknowledged.
Like I said, I hope he gets closer to all of them and that he has a craving for community, but I guess we'll see when season 3 comes around.