I have no experience with this so feel free to ignore everything I say :) but what my intuition tells me...
First throw your guilt out the window. What has happened is in the past.
You have a gift in the sense that you can be there and help someone during the hardest part of their life. You have the opportunity to say things that many people never get to say when their loved ones pass unexpectedly.
If it is uncomfortable for you to call, good. Call. You are giving her an even greater gift by putting your own feelings aside. With all my heart I say be uncomfortable. Be there for her.
Get a sitter and go visit her. Or plan a short visit with your boys. The wonderful thing about children, especially young children is they force you to give them your attention. I bet it would be a welcome relief for her to be with the kids and not thinking about her illness.
I think in this situation many people are afraid to talk about death and what is happening but I say do the opposite. Talk about death...not in a morbid horrible way but have a conversation about it. Where do you think we go? What happens? Of course talk about her life. What does she feel she has done right? Wrong? Regrets? Highlights? Learn something from all this. I'm sure it would make her feel good that in death she is helping you learn about life. That's what life is all about anyway - to learn and to love.
Have your boys draw her pictures. Send her some every couple days with a little note from you. Call her if even it's just for a minute to ask how she's doing.
Don't do anything out of fear of regrets. Fear should never factor in the equation. Do everything out of love. The biggest gift you can give someone is to go out of your comfort zone and do something 100% for them. The harder it is for you to do, the greater the gift you are giving them.
Good luck to you and my prayers to your cousin.