Your mother has it all wrong- your brother is HER responsiblity - you are the sister- not his mother - you have done what you can & you have done plenty - it is sad that this is happening to him but he also has to take responsiblity for his own life especially since he has a child depending upon him. Do NOT forfeit your life for his - that is not fair to you.
Actually, the 29 year old adult father of a child should be responsible for HIMSELF. But I agree with everything else you said.
UPDATE**** WELL WWIII has officially erupted.My Mom decided to hit below the belt further and told me I had No buisness going to Disney in Sept when my brother may be dying

.I told her I was going to WDW and that if we don't go, she can kindly be the one to break the news(the truth)to my 4 y/o daughter.I told her that he is not my responsibility .She told me I should postpone my trip ,till he is better and then we can all go.no sorry, already postponed the trip once for a family trip that never happened.My Dad took my side and now him and my Mom are at each others throats.So who knows where this will end up.I thinkI will screen my phone calls for a few days till this calms down.I did find my brother a Oncologist referral, but he is adamant about not having Chemo or surgery and already missed one oncology appt ( with his original dr)because he did not "feel well".I don't know many Cancer pts that do feel well.
First of all, my prayers for your brother's health and recovery.
It sucks being the oldest. I'm the oldest of 3 also - my brother is the baby and we have another sister. He was coddled his entire life because he was the baby and the only boy. As an adult he's had a million different jobs because he quits as soon as something gets a little difficult or he has to work a little harder because he's used to having things handed to him by my mother. My dad wasn't as bad, but he caves whenever my mom has to bail out "the baby" again. My brother's married to another youngest of three, and she was the only girl, so she's as bad as he is.
I think being the oldest, you're just expected to be the one that takes care of everyone and everything. My brother can treat my parents like crap, not visit them for months even though he lives close, not call them for weeks (unless he needs something) and that's fine. I don't return my mom's call for 48 hours and she's like a lunatic.
Your mother was probably the one that "created the monster" so to speak, and it's completely unfair to expect you to have to keep it going. If your brother isn't mature and responsible enough to take care of his own health, there's nothing you'll be able to do for him by physically being out west versus being here and taking care of your own family, which is where you should be.
And please don't let her talk you into cancelling your trip. Obviously should the worst happen to your brother while you're away, you'll come home. But you can't perpetually put your life on hold because your mother tells you "your brother may die". Obviously as an oncology RN, you know that every cancer is different, some slow, some more agressive and I won't pretend to know what type your brother has. But in the mean time the rest of the family can't be held hostage by it either. My mom was diagnosed with stage IV breast cancer last year. She's doing extremely well right now, but at some point in the future she is going to die from her cancer. She does not expect us to cancel our vacations or (in my sisters case) job relocation because she has cancer. We do what she needs us to do, but we continue to live our lives.
If you want to go out for a week, check up on him, talk to his doctors, try to get him on the right path, that's more than enough. Any further coddling needs to be done by his mother.