Hi K.,
I'm confused about your daughter's comment that you're not her mommy... Are you a step, adopted, or foster mom? Or is she implying that because you weren't 'nice' you must not be a mom?
You didn't mention other incidents, so I don't know what you've done in the past. Nor do I know much about your home life. Because of these missing details, I don't know if this advice will be helpful or not.
First of all, raising your voice back to her only confirms to her that raising your voice is the way to respond when frustrated about something. I suggest calmly commenting that your family is doing something together and thus it is ok for either of you to hold the cart, push it, etc. I'd also add that you ARE nice to her. Everything you do for her whether it is feeding her, buying her clothes, etc, is because you love her and knows she needs it. And EVERYBODY deserves kindness and love.
One more thing. You mentioned self-control for both of you. Although I don't know how much you have or your experiences, I know that she will learn your behaviors from you. In other words, act as you'd like for her to act so she has an example to learn from. If you get frustrated and loudly verbalize your frustrations, so will she. If you advance your level of self-control, you will be able to use yourself as an example. She will then have a positive role model, as well as a mom, to learn from.
Hope this helps. Good luck.
J. Graybill
Stepfamily Coach
Sensible Steps
Solutions for Today's Families
http://www.sensiblestepsolutions.com
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