Out of these two minorities, is either one dominant?

Most likely you are going to get a redhead no matter how you look at it!

All my babies were!

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Just another SASSY redhead that doesn't take crap or like drama!

My daughter ended up with brown hair with red highlights.  When she was little, it looked a lot redder.

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Live free or die

from what i have read, blonde is dominant over red, but you will probably get a strawberry blonde. 

I have naturally dark blond hair, it gets darker as the weather gets colder, and lighter when its hot, my eyebrows are different mixtures of dark and light blond and my leg/belly/other hairs are very light, so at first glance I look like a blonde; but my beard is ginger. And I mean proper ginger. So no; neither are from my experiences.