Someone else's action should not determine your response. - Dalai Lama
First your statement of "Don't react. Do respond." fits in just fine with the above quote. The response that the Dalai Lama is talking about is a response based on YOUR BELIEFS versus based on the someone else's actions. The only way you can have any hope of following this advice is to really know who you are and who you want to be. Otherwise you will feel like you have to respond based on the other person's actions.
you could smile at me and say "Would you like some ice cream?" and I could choose to spit on the floor and mutter "Wallpaper. Zebra. Electricity." and my behavior/response would be in alignment with the [Dalai Lama's] statement.
Yes you could choose that and what would your response to my smile and question indicate to me about YOU? If that's how you want me to see you, then you are free to choose that response. (Of course most people that respond like this really aren't "choosing" to!!)
Think about it from this direction. Our responses in life are always about who we are. Once we decide who we are and how we want to act then we set about acting that way regardless of other's actions.
Can you imagine if Gandhi or MLK Jr. had said that they believed in non-violence but only if people were not violent with them? Their strength and power came from their conviction of standing true to their beliefs regardless of what others did to them. It's not easy and it certainly doesn't always make sense to others.
There is so much more to say about this AND about Burgbud's comments about the difference between a wife's "testing" and out and out abuse. I just don't have the time!!
But what is happiness except the simple harmony between a man and the life he leads? ~Albert Camus