This OP provides a possible explanation: https://www.democraticunderground.com/100210780668

SPOUTUS said it is aimed at the "fake media;" Melania handlers said it was just a Jacket, a fashion thing. People have speculated everything from she is a fascist to it was a dig at her husband.

Personally I think SPOUTUS made her wear it to allow her to both show compassion while dog whistling his Nazi supporters.

She wore it to board the plane, took it off for the visit, put it back on--in sweltering DC weather--for the trip back to the WH. It was clearly intentional--she's never owned, much less worn, such a cheap article of clothing since she married Donald Trump, plus she's an ex-fashion model who is as clothes-conscious as any fashionista--but the message wasn't directed to the children. Maybe about the children, but not to them.

My opinion is that she's another RW troll, like Ann Coulter and Corey Lewandowski, who delights in causing liberals to screech and over-react. Her husband says the message was to the Fake Media, which is bullshit of course, but there was a message. Her fluency in English will help her, no doubt, explain exactly what she meant some day. Until convinced otherwise, though, I believe it was a childish, trollish poke at us.