Great post Grace.
I really feel for you Jud. I think you are going to have to prioritise.
It sounds harsh, I realise. But it's necessary.
Right, first is YOU. If you don't put yourself first you won't get healthy, it's as simple as that.
So make sure you have daily time outs for yourself. Are you a member of a cancer support group? They can be really good. Ask your GP, or alternately you could join an online one.
Right, next are the boys. They are children and therefore come before your daughter. The best thing you can do for them is to love them.
Spend time with them doing new things, cook with them, craft work, feeding the ducks - all the fun stuff that their mother is probably too wired to do with them right now.
Third on the priority list is your daughter. As a healthy adult, she has to come after you and the boys.
Please ask her to attend counselling. (I assume) You are not a counsellor. You can't be expected to say and do the right thing all the time.
I know as her mum you want to 'fix' this for her. But you can't.
She doesn't sound that she is acting entirely rationally at the moment.
BUT that doesn't mean that you can't have boundaries. Next time she is rude to you I would say something along the lines of "I know this is hard for you and I will help you in any way I can. I love you, but please don't be angry at me."
Try to get her to focus on the boys, rather than on her butthead ex.
Praise her parenting. Praise her children. Praise her.
All the best. You are being a good mum.