I am 91 years old and am thinking of getting an Apple Watch . My children have iphones but no watch. Will they be able to be notified if I fall?

There is an option to use Family Setup if you want to have a watch but not a phone. The watch though initially has to be set up on one of your family members phone. See details here: https://support.apple.com/en-us/HT211768

This may help guide you as to how fall detection works https://support.apple.com/en-us/HT208944

I don’t think connecting your watch to someone else’s iPhone is going to be practical.