Poor mom. She's totally overwhelmed and trying to glue her life together, and having kids and having to work and carry the entire burden, and not being able to afford a babysitter.

Calling 911, next time the smoke detector goes off, good idea, as well as possibly calling CPS. However, I'm gonna suggest maybe stepping in as a friendly helping hand. I'll probably be downvoted, but, as someone who lost an SO, I know the pain she's gone through and I feel like she needs some love.

-Damn dog needs to be leashed, if he goes outside, perhaps suggest a leash (and buy one? They're like ten bucks and you dont have to deal with it again) and mom can clip it to the door so he doesn't sneak into your yard. Heck if he snuck in I'd do it and just place him back, with the leash. Hint hint. The barking, that sucks. I don't know how to avoid that.

-CPS should be called, but as a fellow human it would be nice if you kept your eyes and ears open if you knew the kids were unattended. Or perhaps offer to the kids to call you if they need help for anything. I know, it's not your problem, but a little kindness goes a long way sometimes.

-Finally, maybe one day, you can reach out to mom and maybe invite her over for dinner with the kids. I can't imagine she has a lot of time to sit and eat a meal someone else prepares.