I am sorry for your loss brother. I was the same as you for about two weeks. But then I gradually started being more engaged because the kids demand it. I’d also like to recommend that you buy this book and read it: A Parent's Guide to Raising Grieving Children: Rebuilding Your Family after the Death of a Loved One https://www.amazon.com/dp/0195328841/ref=cm_sw_r_cp_api_i_N1ftFbSSD4FZF
There is a lot of good guidance in it. It is not a happy book, but it will give you some things to focus on and answer some questions you no doubt have as the parent of grieving children.
First, I am sorry to hear about your wife. Having just gone through it with my wife a year ago, I very much can empathize. My wife (48) was diagnosed with a GBM. She was given weeks to live without immediate radiation and lived exactly one year and one week from the day the tumor was discovered.
Like you, I worried a lot about how my daughter would handle it and what the long term consequences of her mom dying would be for her. I was candid with my daughter about what was going to happen from the start (I would not have been if she were 6). And she held up pretty well until my wife started to decline which coincided with the start of the pandemic.
Here are some things that I learned over that time that may be helpful:
(1) Don’t refer to your wife as “sick” to your daughter. She won’t understand the difference between normal “sick” and terminal illness and she’ll fear sickness. Use the term cancer.
(2) A lot of cancer centers have therapy/counseling/support for children of cancer patients. If yours doesn’t, seek out a therapist for your daughter, for yourself, your wife, and for you as a couple.
(3) Ask if your hospital has interpreters.
(4) Talk with your wife about your and her fears. About what she wants for you and your daughter.
(5) I bought this book and read it in the months leading up to my wife’s death. I found it useful:
A Parent's Guide to Raising Grieving Children: Rebuilding Your Family after the Death of a Loved One https://www.amazon.com/dp/0195328841/ref=cm_sw_r_cp_apip_FKIdBSwkHRtjV
(6) Make arrangements with hospice now. Involve your wife. It’s a lot harder to do (emotionally, practically) when you’re at the time you need it.
(7) Just try and take it one day at a time. Try to find something to be happy about. It will get worse before it gets better. A phrase that I started saying in the last few months of my wife’s life was “It is what it is.” There really wasn’t any other way to think about it and stay sane.
(8) Understand as the cancer starts to win and your wife nears the end, the cancer, drugs, and fear of dying may make your wife act in ways and say things that hurt incredibly. For example, my wife, angry that I agreed with her doctor about the need to enter hospice said to me “You just want me to hurry up and die.” But know, that’s not her, and she loves you.
Feel free to DM me if you just need someone who has been in your shoes recently to talk to. I am happy to just listen and provide support.
One last thing, I forgot to include: with your daughter only 6, you are lucky in someways. She is still very much a kid and you’ll find she bounces pretty easily between sad and normal kid. I’d much rather have my daughter be that age than entering into her teenage years and dealing with this stuff like mine is.
I can only pass along my experience (married 12 years, 11yo daughter and 25 stepson).
If you're like me at all, you'll find that you return to the normal daily grind pretty quickly: you'll go shopping, make meals, do chores, etc; because you have to. But there will be days where you don't want to do any of that stuff. It's okay not to, sometimes you need days just to tune out (obviously there's a limit, you have a kid). But you'll also need to work hard to avoid letting 'tuning out' become a habit, because, again, you have a child. I find trying to get at least one thing that needs to be done a day to help with that.
I find myself experiencing a lot of private grief. When I'm around my kids it's kind of just normal except my wife isn't around. But in quiet moments I feel her absence exquisitely and I weep.
All that said, seeing as you're in the military, it maybe the structure of that life helps you with the above.
From a parenting perspective, here are the things I find hardest to deal with:
I highly recommend getting a therapist for yourself and a child. Lastly, I really found this book to be helpful.