I just don't know what to do.

I so understand your dilemma - it’s one I’ve experienced many times myself. Unfortunately you’re going to have to prioritise your family’s and friend’s needs according to what is practical.

You mention that your friend has a big social circle, so in your shoes I would try to squeeze in a visit to your friend and use that time to contact the people in her social circle and arrange a rota of willing people who could each take on a particular task. If a visit is too much then it could be done via a WhatsApp group, which I recommend you set up anyway. The important thing is not that YOU have to do everything yourself, but that your friend has appropriate support. Explain your dilemma to your friend and show her that you have a solution and hopefully she will be understanding.

As your friend is also your children’s godmother I would include them in the WhatsApp group too, for two reasons: firstly so that they are aware of how much you’re juggling, and second so that they can offer support to both of you. Things like letterbox ‘care’ packages, flowers, or a card only take a minute or two to send and need not be expensive.

Lizbethann , It’s all going to sort itself out, if you put yourself first, your family next and then your friends . Your friend with cancer will have a care package in place - I’m sure the Hospital will organise this, especially because, she is on her own. My friend who is on her own, will be discharged next week, post op,(femur fracture) and will be having a Care Package, which will be FOC , for 6 weeks, and after that, if she still needs it, she will have to pay for it. I live only 2 doors away, and will visit her and make as many cups of tea as she needs, but won’t be doing much else. She has a niece who works full time and so can’t do much.
You have got enough on your plate - so don’t feel guilty

Oh dear, you are in a pickle.
I think you should explain your situation to all parties concerned first and check out their reactions.
Your friend will have a set date for her operation so it you let them know when you'll be unavailable it gives them time to get alternative care arranged - if its needed.
Most people are reasonable, and your daughter may be able to call on other friends/relatives to look after her family when the time comes. Mums are out of the delivery room and straight home these days and she may be co-operative.
Or she may not of course.
And babies arrivals are unpredictable ........
There is no easy solution.

Oh dear, Lizbethann55, how awful for your friend!
But, just as awful as it is for her, surely she knew it would be very difficult for you to just drop everything and go running to her?
Is it at all possible for her to come to you and have her chemo etc at a hospital close to you? If not, then I'm sorry but you're just going to have to let her down but gently! Tell her you made a promise to her without putting your brain in gear first, or else you would have remembered all these other things you had already promised to do, which I think should come first!
Tell her you'll visit her whenever possible, but you just cannot look after her like you thought you'd be able to, and say that she must ask other friends and family for the help!

Does your friend have email? I started emailing one of my friends each evening during the time that her husband was dying. It meant that she could respond when it was convenient. We've maintained this habit now for a number of years, usually just reporting on what we've done each day. We both look forward to our daily "chat".

Maybe, when you can't actually physically be there for your friend, a regular message would help her to keep positive, whether it's an email, a text message or a phone call.

Sending her your thoughts when she has an appointment and checking up on her afterwards might help both of you.

And, of course, see her when you can.

You've a lot to deal with at the moment, and can't do everything, but maybe something like I've suggested will be manageable.