"Passet dit", "Mine barn"

In Norwegian 3, I have the following examples:

“du må vise passet ditt på flyplassen” meaning “you have to show your passport in the airport.”

I also have:
“mine barn trenger ikke flere spill” meaning “my children don’t need another video game.”

Is it wrong to say “Barn mine” instead of “mine barn” at the beginning of a sentence?

Yes. You have to use the definite article in that case: barna mine.