<<Disclaimer: Verify this information before applying it to your situation.>>

Thanks everyone for your suggestions.  Several people mentioned the Earth's Balance buttery sticks.  They sound interesting unless they are made from soy which I don't eat.  I haven't tried anything new yet, but I did make the BC cookie mix with some butter and mostly oil and they came out delicious, although not as good as with all butter.  
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I use coconut oil for all our baking: it's cheaper than butter for 
one thing, and it doesn't go rancid like vegetable oils. Most
vegie oils (esp. canola) are not very good for you. Anyway,
you can get it by the gallon from WildernessFamilyNaturals
and it tastes marvelous (the expeller pressed does not taste
like coconuts at all).


If a recipe uses butter though, you need to add just a tad
bit more water and a tad less oil, since butter has some
water in it. I can usually just eyeball it though, at this point.
Why not contact them for advice. It would help everyone.
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Try and find the vegan Earth's Balance Buttery Sticks.  I use them for all baking and can't tell the difference usually from real butter.  Non-hydrogenated and non-artery-clogging......I find them at the hf section at Kroger and also at Whole Foods....great sub, esp. for dairy-sensitive people and people wanting to save their health from being decimated with butter etc.
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The mixes (like other cakes with butter) rely on the air whipped into the butter to raise them. So if you don't beat margarine or butter, you won't get as light a cake or cookie.
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yes, apple sauce, grated zucchini works well too.
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I've only made the Betty Crocker cake once, but when I did I made it with a can of pumpkin.  All you do it add canned pumpkin (regular, not the ready for pumpkin pie variety) and mix it with the flour.  You don't need to add anything else.  I used this for the yellow cake mix and while it looked a little orange, you couldn't taste the pumpkin.  It was super moist and soooo delicious.  
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      I haven't made the Betty Crocker mix yet, but I always substitute either shortening or coconut oil for butter in recipes since we are dairy free and gluten free.  I usually use shortening unless the recipe calls for melted butter.  I have never had a problem doing this
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      Pamela's gluten free mixes have recipes that use oil instead of
      butter, and they are fantastic.
      I have used applesauce in addition to oil with them 

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Have you tried Earth Balance buttery sticks? It works as well as butter and is non-dairy. 

The mixes (like other cakes with butter) rely on the air whipped into the butter to raise them. So if you don't beat margarine or butter, you won't get as light a cake or cookie. 
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today  i made the yellow cake:

1 box mix
1 20oz can crushed pineappel
2 eggs
1 tablespoon vanilla.

turned it into the most delicious cupcakes.
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I don't use any of the oil/butter.   I use applesauce all the time  
instead of oil.
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My kids suggested that I use fat free Greek yogurt instead of butter. Worked wonderfully- cut the sweetness and the calories. Doesn't help with your dairy situation however. We also used egg beaters
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I know you said you don't really use dairy, but non fat plain or vanilla yogurt a soy version maybe. 
That will most likely make more like cake then a traditional brownie. Goodluck

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