Lena Headey -- the hot chick in "Game of Thrones" -- says her estranged husband is too reckless to care for their kid, and a key example was Peter Loughran's decision to post pictures of himself showcasing an AK-47 . . . this according to legal docs obtained by TMZ.
Lena was trying to block Peter from taking their 2-year-old son to Ireland. In her legal docs -- filed in her ongoing custody war with her ex -- Lena says Peter has exhibited bad judgment and cannot be trusted alone with the boy.
As an example, she attached 2 pics to her docs -- ones that Peter allegedly posted on his Facebook page, showing him sporting an assault rifle.
She also claims Peter -- a one-time hairstylist -- has serious alcohol issues, citing a recent case where his car veered into oncoming traffic. She believes it was alcohol-related, but he denied it.
The judge sided with Lena and refused to grant Peter's request to take the kid to Ireland.