It is actually fun to compare Mary and our Marie and their approach.
Marie to this day use fairly simple expressions and simple sentences, which is probably a sound idea and very useful for fairly non-committal conversations.
Mary on the other hand had to, (and wanted to) take on more complicated subjects and also convey more complicated subjects. And that meant that she used more complicated words to get her exact meaning across. Using a word like "voldsudøvende = someone committing violence" (from a documentary) which is difficult for us natives!
Mary admitted that she initially tried to translate what she meant to say directly from English to Danish - and as you probably know, that doesn't work.
It's my impression that Mary has charged the Danish language head on, and on a fairly advanced level, while Marie use the school-approach: This is a cow. The cow is brown. Cows eat grass. - You get my meaning?
And then there is the little thing about local accents. Mary speaks with a distinct Copenhagener accent. Or Northern Zealandic accent perhaps.
Marie speaks with a slight southern Jutlandic accent, as nwinther pointed out.
Now, over the years I have been contacted by several who wanted to learn Danish and they have later said that people speaking with a southern Jutlandic accent are much easier to understand. One of them, an American, attended a class at university and she had a Danish teacher from Copenhagen. She had problems understanding spoken Danish. So she was allowed to use a YouTube video of a former PM delivering a New Year speech as a part of her examen. He spoke with a distinct Southern Jutlandic tone. She found that he was much easier to understand - and she passed.
- As a native I am not in a position to say why the PM is easier to understand than QMII delivering her New Year speech. But I can well imagine that I would find it easier to understand someone from Boston than someone from New Orleans, who are saying the exact same thing.
Then there is the spouse-factor. You of course learn most from the one who is closest to you.
And we don't know about Marie's approach. Perhaps she used the approach of asking questions all day long to the point of Joachim waking up at night, bathed in cold sweat, screaming: "It's a sheep. The sheep is white. Sheeps taste...ehh".
Alexandra on the other hand has admitted that she and Joachim did not speak Danish that much together initially. "It would be a teacher-pupil relationship" as she put it. But she has an interest in languages and she has a German speaking mother. That probably helped as no one can put a finger on Alexandra's Danish.