As written by GHH member, frosta

Brenda literally went from blowing out her birthday candles, knowing she'd wished for the impossible, to someone walking up and handing her that very impossible dream.  As infuriating as the whole situation is she can't avoid her strong desire to embrace the impossible.  It's the magic fix for a nightmare that has haunted her for years. 

While, as a viewer, I want to absolutely scream at the idea of a DNA test not being done, if I try and "put myself in her shoes" I can see the more irrational and emotionally driven desire to hide from the truth. This is especially so when you start to look at Brenda's nature.  It's already been stated that she "hides her head in the sand" in regard to the mob business, so it doesn't seem that surprising that she would want to in other situations.

I want the DNA test done because I want to know what's really going on (we've only been waiting 8 months!) so I'm sure I'm going to lose it when she unloads on Sonny for suggesting it, but I still get why such a fragile woman would want to cling to her fantasy, even if that means avoiding the the truth.   (I am going to try to avoid the rant about how disturbing and depressing it is to me to describe Brenda as a "fragile woman.") 

What's actually more mystifying to me than Brenda refusing the test is Sonny not going behind her back to get it done himself.  Can't he just pull a hair from each of their hands and ship them off for comparison??  I know the story hasn't reached a point that would justify that, yet, but it seems like an obvious solution - at least until his theory is proven correct and he gets to not only tell her Lucian isn't hers but that he went behind her back to prove it.  (Those would be some fun fireworks, lol!) 

Perhaps that idea is more tied to me wanting to know who the kid really is rather than any kind of logic.