I am so sorry to hear about your mother's diagnosis. Having just gone through this myself (the news came only two months after BD) I know how hard these next few months will be for you and your family.
During my parent's illness, I received very little support from my xSO. So I drew my support from others who all needed to draw support from me. I don't know if you have a large extended family or if you are an only child, but much responsibility will fall to you. Be as present as you can while she is able to function. Try (I know how hard it is) to forget about what your ex-W is doing. Keep your children informed of thier grandmother's progress, if they are not able to visit.
Laugh when you can; your mother will appreciate it as well. Let her take the lead.
If your ex-W wants to ask your children how their grandmother is doing, let her. They may need to talk about it. There is no propriety over grief. Don't insist that she talk to you. Antonia's post is spot-on.
This is going to be hard, Tad. Our thoughts and prayers are with you and your mother.