I am going through the same up and down feeling about my Mum's cancer. She has liver cancer and her prognosis is two years. Some days I am coping, some days I am positive, and other days I'm teary and depressed and not sure how I'm going to get through it. I'm throwing myself into my CFA training the same way you are throwing yourself into work.
I have a friend who did the same thing when her father had cancer and she said she doesn't know how she would have survived that time if she didn't have something to distract herself with.
I figure that as long as the thing you are throwing yourself into brings you pleasure or gives you some sense of purpose and helps you forget and enjoy life a bit then it's a healthy and good thing. Especially if they are aware and are a compassionate support for you. I know that training for me is such a respite. I completely forget everything else for a few hours each week while I learn to bowl a hose or hold a long-town branch. I feel my immune system needs those times, otherwise I'm going to run myself into the ground with worry and my children need me. Your bread winning role is so valuable in this situation. You are doing something really practical and purposeful to help. I think the danger is probably if you are finding the escape is robbing your family of your much needed emotional and physical presence and support, and if it's becoming a hindrance to really processing what's going on properly so that you yourself can deal with it.
Having said that, I've also confronted the issue head on and read all the literature. I know what is coming at the worst. That was hard to do and I ended up very depressed but I figured that if I deal with it in small stages, then I'm preparing myself somehow and making me more able to support Mum. I'm dealing with it in little stages, because what else can you do?
I also live a long way away from Mum so can't support her directly. I support her by contacting her every week so she can offload to me and talk to me in regard to her fears and worries and hopes. I read the literature she reads on healing cancer and support her in her decisions to fight it and don't burden her with my private worries. I love her and make sure she knows I am there for her. That's the best I can do from here.
I am so sorry for your daughter's diagnosis. it's so hard. I had a cervical cancer scare a few years back. It's good to hear her blood count is up though, and she is very lucky to have such a loving father.
The above is no professional opinion, simply how I'm coping with a loved one with cancer at this stage in my journey.