Being a stay at home mom (SAHM) does not leave me a great deal of this "quiet time in a busy life, time to reflect or just be free of demands." but it is a key part of being a SAHM to maintain sanity.
It is suggested when you have an infant and you feel overwhelmed at any moment, even when they are screaming/crying, that it is okay to step outside for a breather. That's how crucial it is to create and preserve peace, that it's "allowed" to abandon your duties for a minute in order to come back productive. I don't take a single moment for granted. I enjoy doing dishes more than could be understood because I like zoning out and staring out the window and tuning out.
I guess to answer your question more clearly, I create and preserve peace in my everyday life by accepting that I deserve it. I don't look for a window of time to find that peace but I demand myself to take the time. If you don't recognize that you owe it yourself, you will convince yourself you don't have time, you'll get overwhelmed and that's it, you're frustrated and distracted and disappointed.
When you have 10 minutes to start dinner, make those phone calls you've been putting off, etc just don't. Sit outside and enjoy some air for 10 minutes instead!! It's okay!