There are some situations in my house in which the end result is non negotiable. Now, the how or when part may be open to negotiation, but in the end, it needs to be done. Like the diaper thing. I have a daughter who is now three years old and has no interest in the potty. OK, fine, when she goes is up to her. She does need her poopy diaper changed. IME girls can't be left in poop as long as boys can. THey will break out faster in a rash or even a yeast infection with prolonged exposure to feces. My 3yo has EXTREMELY sensitive skin. She will literally be red within 10-15 minutes of pooping. This is not an exaggeration. She must be changed. I will negotiate how or where she is changed, what I use to wipe her butt, she picks the new diaper, etc. But, in the end she needs to be changed. Her only real alternative here is the potty.
Toothbrushing also needs to be done. This may not be as important at 1 or 2 years old, but my oldest is 8 and she has grown up teeth in her mouth. To allow them to rot would be irresponsible of ME as a mother. She may not want to do it, but doesn't really understand the long term implications of never brushing your teeth or seeing a dentist. Although I have commented when she notices someone with rotted teeth.
She can choose which toothbrush to use, which toothpaste, or choose to let me do it for her or do it herself. In the end, it needs to be done.
Homework needs to be done. It is expected in their school and important to help her understanding of the work. The 2 that are in school can choose when and where it will be done. They can do it right after their snack, watch tv first, do it before dinner or after dinner. But, it needs to be done.
The only real non negotiables at all are running in the street (DUH) and not beating the crap out of each other. Whether they agree or not, they may not smack one of their sisters in the head. Oh and my 3yo has one more non negotiable. She is NOT ALLOWED to drag the kitty around the house by the tail. EVER.
The kitty is a creature with the right to be safe in our home, just as she is.
It seems that some people equate non negotiables with force. I don't drag them into the bathroom and shove a toothbrush down their throats. I don't tie them to the kitchen chair and tape the pencil in their hands. They know the expectation. They understand the limits, as to when things must be done. In general, they abide by these happily. I can think of very few situations where actual force has ever been used. Just explaining the expectation and asking how or when (depending on the situation) they would like to do it, has been enough for us. They really do respond well to this.