It’s hard in those early days especially when you get a rude awakening like being in the hospital. But you’re absolutely right that there’s a reason to be here and a reason to press on: not just your kids, it also yourself and your life. There is value in life and you’ll see it more and more as you work your recovery.
Try reading up a bit and learning what you can while you’re recovering:
Keep checking in here and stay focused. Share share share your feelings and experience - you’ll be surprised the difference it makes