Are the armor equips that you've improved better than her Steel Plate armor that she wears?
I would think. It's steel improved to Exquisite.
If you want your follower to sleep in a bed, just talk to them and select the "I need you to do something" command and then aim your cursor at the bed.
I tried that a while back, but if I remember right, she seemed to think I was talking about someplace downstairs. I'll give it another try.
The armor you're giving her might not be better than hers in terms of protection, even if it might be that you're giving her Daedric. Might be a special set specifically for her or something to that effect.
I gave Borgakh all Ebony gear that I improved for her and she chose it immediately over her original Orcish stuff.
Huh. Yeah, all this should be better than what she has. She uses the weapons I hand her, she uses the helmet I gave her and I handed her an improved (Superior) Banded Iron shield and she uses that over the regular Iron shield she normally carries. So then I went and improved a set of Steel Armor, Boots and Bracers and game them to her, but she won't wear them.