Reddit mentions of The Invisible String

We dealt with something similar where BM would smother the SD's constantly when they were over there, so any time they came to our house they weren't used to not being taken care of constantly or having a cheerleader shadowing them all the time. Which meant any second they had to themselves to think, they immediately went to "I miss mommy". It was sooooo frustrating, and it took SO a long time talking to them about how it was perfectly ok for them to do their own thing sometimes. That they are getting older and as such will need to be able to soothe themselves out of discomfort. Their feelings are legit, they are allowed to have them, but we couldn't let them just wallow in misery the whole time. We'd also focus on positive things when they'd come over, like what their favourite part of their day was, what made them laugh, etc.

Maybe look into some books on feelings, missing the other parent, growing up. The Invisible String is a good one. SO spent a lot of time during the bedtime routine, which was usually when their anxiety and "I miss mom" was the worst. He's STILL doing the same routine now. Just letting the kids know the routine, know what to expect, and having that predictability really helped.

As you said, definitely a good idea to wait until you have a more definitive prognosis, but there are some resources I can suggest for when that time comes. If you end up with a cancer diagnosis, or actually even if you don't, I highly recommend the picture book Let My Colors Out - it briefly mentions that the mom has cancer but mostly just refers to her being very sick, so you could skip the cancer sentence and it would work just as well. Most of the other cancer books focus on aspects of treatment that may or may not apply to you (hair loss from chemo, etc) but there also a few books that explain long-term parental illness more broadly which might be worth checking out, such as Mommy Has to Stay in Bed and Mommy Can't Dance. None of these touch on the idea of terminal illness, however. There are only a couple picture books I'm aware of that show both before and after the death - The Fix-It Man is a beautiful story of a little girl who thinks her dad can fix anything, until her mother dies of an unspecified long-term illness and the girl and her dad try to come to terms with the loss; and Ida, Always is a story about two polar bears who are best friends until one develops a terminal illness, gets increasingly sick, and eventually dies. Both are obviously pretty emotional stories, but manage to end on a note of hope and healing. There's also a very simple activity book called Help Me Say Goodbye to help children understand terminal illness and cope after their loved one dies; it's designed for slightly older kids but would definitely be something a 4yo could work through with you and your partner.

There are other picture books that take place immediately after the parent's death, such as The Garden of Hope which shows a father and young daughter coping with the loss of her mother; Missing Mommy which is told from the perspective of a very young child trying to understand where his deceased mother has gone; and The Scar, also from the perspective of a young boy whose mother has just died (the opening lines are, "Mom died this morning. It wasn't really this morning. Dad said she died during the night, but I was sleeping during the night. For me, she died this morning.") This last one may not be appropriate for a 4yo, as it's longer and more complex, and quite emotionally intense. There are also a few picture books that I feel are a bit more aimed at the parents than the children, but may be meaningful to you - A Bubble, which was written by a dying mother to her two-year-old daughter, and Only One of Me, which was written by a mother to her children upon receiving a diagnosis of terminal cancer.

And of course there books that help children understand and cope with death of a loved one more broadly - for a 4yo, I would recommend I Miss You: A First Look at Death as a good non-fiction explanation and The Goodbye Book for a very simple look at the feelings that come with saying goodbye when someone dies. I also really like the book Life is Like the Wind, which explains death as life leaving the body the way wind leaves a kite and causes it to no longer fly; it does a good job of concretely explaining what death means and how it feels to lose someone you love, and also briefly explores different beliefs about what happens after you die ("People have different ideas about where a life goes when it leaves the body. Some people believe the life enters another body to give life to a new creature. Others believe life goes to a happy place called heaven, where the life can enjoy its favorite things. Some think life goes deep into the ground, giving new life to trees and flowers, or that life goes way up into the stars, where it twinkles brightly and watches over us.") There are also some good books that focus on ways to remember lost loved ones, such as The Memory Box, Here in the Garden, and Always and Forever. There are also several other activity books to help children process grief, such as Muddles, Puddles, and Sunshine and Why Did You Die? Activities to Help Children Cope with Grief & Loss.

Lastly, I'd like to recommend two books that aren't about illness or death specifically but might be very reassuring to your daughter, and you could start reading them now in any case - The Invisible String and No Matter What. The latter has both a UK edition and a US edition with slightly different text, most notably the endings; the UK version includes a line about love continuing after death, which the US one sanitizes into just "when you're far away" - I recommend taking a look at both versions and deciding which you prefer (here are youtube videos showing the US version and UK version). There's also a workbook/activity book coming out in a couple months to go with the Invisible String book, so might be worth checking that out too when it's available.

I hope all this information isn't too overwhelming - feel free to save this post for a time when you feel up to dealing with it, or hand it off to your partner to sort through. Hopefully you'll find something in here helpful. There are also lots of good resources online to advise you on how to have these conversations with your daughter; I'd recommend checking out the comments in this recent post for some good links. Especially be sure to check out the Sesame Street resources on grief in young children, lots of useful stuff in there. I also definitely recommend both you and your partner speaking to a counselor (and your daughter too eventually). I can't imagine going through something like this, and while I completely understand the guilt you feel, I really hope you can find ways to let go of that and enjoy the time you have left with your family. Wishing you healing and peace.