As a person who has been on the children's side of this type of story, here are my thoughts. My mother was diagnosed with stage iv lung cancer when I was 23. She was divorced and living alone at that time. There was quite a bit of time when my sister (21) moved in to help her and I also stayed with her when possible (I was living out of state at the time). I stayed with her for up to a month at a time.
It is great you are visiting and helping out when possible. They are probably quite thankful, especially for your friendship and time. I would talk with the mom about whether or not you should enlist the kids help. Yes, they are "old enough" to help out, but they apparently haven't been asked to in the past and right now they are going through something EXTREMELY difficult.
At times like these, people need to be the priority - not cleaning, dishes, laundry, etc. Of course, those things have to be done when they can...but the whole family should really be concentrating on spending quality time with their mother. The laundry will still be there tomorrow. Their mom may not. Long term survival rates for lung cancer discovered this late in the game are VERY poor.
As a neighbor that has known the family for less than a year, I would approach this subject cautiously. The children may take your suggestion the wrong way and close off. Honestly, it could affect the way they even interact with their mother..feeling like they are not doing what they "should be". They may simply shut down...and this is not the time for that. They need to be "present". Be a listening ear for them, take over meals, personally help when you can, but don't lecture. Let them know that NOW is the time to spend with their mom. They should be taking advantage of every minute they can.
Two years after my mom passed away, my father-in-law died of a brain tumor. His wife, who normally kept a spotless house, slacked on some of the cleaning. She felt guilty about this, but the family soon adopted the saying, "If it doesn't breathe, it doesn't matter." Take care of the people (and pets) during times like these. The rest will still be there when it is all over.
PS I personally think the father should be doing some of those things...but, again, this is not the time or the place to lecture him about his "responsibilities" either.