Just before bedtime my daughter brought me her water bottle and asked if I could fix it.
The button and stem, on the right, are what release the valve so water can flow. It's from a $7 Contigo water bottle, so no big deal. I offered to go get another with her before school tomorrow, but the she said the magic words. "Can you make a new one on the 3D printer?"
Yes Daughter, yes I can.
So I modeled it in Fusion 360:
Then printed it out and viola! One functional, if not very attractive, replacement water-bottle button.