Maybe an offer to help (for a reasonable amount of time) is in order. This is hard to approach her with, because you are basically saying "your house is a mess to the point we are worried", but done well, you can express concern and make the offer.
Or you could call CPS and request a welfare check. It does sound like someone needs to be looking in on her. I've seen similar circumstances with people who are clinically depressed or suffering mental illness. Their children need to have another set of eyes keeping track of them, esp. as they are not in the school system.
Just out of curiosity: was it 'her turn' to host the meeting, did she offer, or was she short on childcare? I just ask because I can't imagine inviting people over for a meeting with a house in such a state. She may need more resources than she has, but may not know how (or have the wherewithal) to access them. This could include health insurance and care for her little ones. Have you met the kids? Do they seem healthy and clean?
I would also be concerned that, if this mom is so overwhelmed she's not doing housework, it's highly likely that school isn't happening. So there's another thing to chew on.
I have one sister who has three boys, homeschools, and her house is relatively tidy (no outside help, like Amy J.) and her boys are doing very well as whole people (health and academics.) I also know of other women, similar to the one you describe, whose bipolar disorder or depression has caused them to take care of the bare minimum and to otherwise shut down. They didn't like the intrusiveness of CPS, but it was better for the kids and they were able to get both educational and other helpful resources.