Can someone explain to me how this work?
den der (det der)
that (one)
denne her (dette her)
this (one)
but then
det her er min mor is translated by
this is my mom why not denne her?
same here:
det her er min mor og far
this is my mom and dad
det der er ikke min datter
that isn’t my daughter ok
dette er min venn fra USA
this is my friend from the United States why not dette her er…?
Your question is surprisingly difficult to answer for a native speaker. I suspect this might be one of those occasions where there might be a rule in a grammar book that is not really followed in everyday speech.
Regardless, to start with the basic distinction between this/that in the sentences you describe is as follows:
den/det - that
denne/dette - this
If you wish to emphasise the distinction, it becomes:
den der - that one there
det der - that (one) there
den her - this one here
det her - this (one) here
denne her- this one here
dette her - this (one) here
As you can see, den her/denne her and det her/dette her are synonymous, and I can’t think of any situation where that does not hold true.
Note however that den/denne can only be used for one - 1 - thing or object.
In contrast, det/dette can be used a bit more broadly, as in the example above with mum AND dad.
Now as you your question about “det her er min mor is translated by this is my mom why not denne her?”, I’ve spent quite a bit of brain power trying to figure out why it does not follow the grammatical gender of “mor”. Frankly, the best I’ve got is that it simply sounds odd to use den/denne for a person or a pet, unless for some reason there is a need to emphasise one. So you might use it to identify your dog in a dog park, but not otherwise. Even then, when it comes to people it sounds a bit dehumanising and would likely be replaced by hun/han. Accordingly, den her/den der might be used humorously if you are e.g. identifying your child at a children’s birthday party, but not as common usage.
Hope the above is helpful!
Thank you so much for your answer, it does clarify a lot for me, even if in practice i might struggle 