In “Norwegian 2” I have these two examples:
“Det her er min mor” meaning “this is my mother.”
BUT
“Dette er min venn fra USA,” meaning “this is my friend from the USA.”
Which is correct?
I’ve never studied the Norwegian language, but it could be the gender of the word? In French there’s 3 words for “a” which are le/la/les. Maybe Norwegian has gender specific words too? Not sure. 
It’s basically the same. “Dette” means “this (here)”, whereas “det her” literally means “this here”. The two expressions are interchangeable, and you will be just as correct using either.
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Thank you, Please.
To elaborate:
“Det” usually means “that over there” as in “Det huset.” which would be “That house (over there).”
Meanwhile “dette” means “this (here)” as in “Dette huset.” which would be “This house (here).”
It has to do with the speaker’s proximity to the mentioned object.
However, adding the word “her” (here) to the phrase with “Det” as in “Det huset her.” basically makes it mean exactly the same as if you just used “Dette”, just a different way of saying it.
Dette huset (This house)
Det huset (That house)
Det huset her (This house)
Thank you.