Everything about her appearance points to that it's Sadie's mother, yes. Not many doubts about it!
What bothers me is that her mom seems to live with her, but in "Lion 3: Straight to the Video", Sadie calls her mom from work to ask her about if she possibly could start making her lunch bags again.
I assume they put it that way because it would take too long to follow Sadie home after work to hear her talking to her mom OR, Sadie felt like talking to her mom right away, being in the fuzzy mood and all after watching the tape Rose had made for Steven.
The message there would probably be that you should appreciate what your mom does for you and that she's usually there for you, even if she can be annoying at times. This is also very important for children to learn, as well as for more grown up people like ourselves...
Lars and Sadie are two of my absolute favorite characters in the show, to be honest. I've watched the episodes specifically about them several more times than I've watched the rest of the episodes, and I've thought a lot about their relationship and how they matter as characters. They are really interesting to follow, and I love them most of all. After Steven, of course.
Anyway, moving on to Lars. As everyone who have actually watched the entire show so far would know, Lars is a VERY insecure character, who cares A LOT about what people think about him and what they might be talking about behind his back. He doesn't want to be talked about, unless it's about something good.. But to be fair, (probably) barely even then either.
If we look back to the episode "Horror Club", we get to take part of a flashback with Ronaldo and Lars from their past, from several years back. I could imagine they're around 10-12 years old at that point? And they're hanging out in their "secret" base.
Ronaldo then 'accidentally' snaps a pretty awkward photo of Lars getting hit in the face by a piece of wood. Ronaldo freaks out and wants to send the photo to the news, saying it's real evidence for paranormal activity, the house being possessed and all that. Lars then takes the photo and rips it into pieces. Ronaldo being Ronaldo, gets very upset over that his evidence is ruined and they start to fight. Ronaldo then yells at Lars: "WHY DO YOU CARE SO MUCH ABOUT WHAT OTHER PEOPLE THINK?!?!" and Lars responds; "You wouldn't say that if you knew what other people say about you!".
In conclusion, Lars have probably heard people talk a lot of shit behind other people's backs. I assume he have heard either his parents gossip about other people, or just other kids in his age. Therefore, he's scared that people will talk about HIM, the way they talk about others.. Which is probably not very pleasant to listen to.
It's still very likely that his parents are busy people, mostly working their bums off, either at home on the computer but most likely somewhere outside town. Just spending most of their time at work or something else. I can believe that Lars really doesn't like his parents for acting and living like this and they have probably never spent much time on Lars either.
OR, he just lives on his own and works to pay the bills, etc. Maybe he's dad an alcoholic, so he felt like he had to move? Maybe he's got a really big family and he's the oldest, so he felt like he needed to move out?(That wouldn't be very likely though, since we already have proof of that Lars lived in Beach City when he was younger) It could be simple, it could be deep. Who knows? We haven't gotten any hints on anything from the show, really. Not much at all about Lars background or how he's holding up with life.
In "Joking Victim" though, we get to see Lars house and it seems to be pretty small, yet quite fancy. He's got a big backyard with a trampoline and everything.
No one opens the door when Sadie knocks on it, so I'd assume that his parents aren't home, if they even live there with him. He's also got game consoles and such too, so... He probably makes enough money with his work for everything to go around??? Gosh, I'm just wildly guessing right now.
ANYWAY.
I'd love to hear and see more official facts about Lars, his past and his family. Hopefully, we will get to see more in the future episodes. <3 Sorry for the wall of text, I could just talk about Lars and Sadie forever.
NOTE: Sour Cream(the DJ guy with the white hair to the far left in the picture), doesn't have his parents close by either. I wouldn't suppose they're out of frame either, I just don't think they're there with him. He seems to be just as old as Lars and Sadie, if not one or two years older. Still, this could be more proof of why it would be pretty accurate for Lars to live on his own too.