From: INFRARED PYTHON | #003 I wish I could get that stupid hat off of her without giving her an even uglier helmet, I just want to see her with her hair down. Is that too much to ask for??
Do you mind sunglasses? Step 1 - Get a full-face helmet, a head-and-eyes helmet, and any glasses/sunglasses/goggles. For this example, we'll use Recruit helm, Ballcap with Glasses, and Sunglasses. Step 2 - Place the Recruit helm and Ballcap w/ Glasses in her inventory. Close the screen so that she equips the helmet. Step 3 - Remove the Recruit helm from her inventory and place the Sunglasses in. Close the screen so that she equips the glasses.
Tada! Don't take the Ballcap or Sunglasses from her inventory though, she'll put the hat back on. Also, if you save and reload and she follows you through a loading screen she'll put the hat back on.