I would start by telling DH to behave himself! He needs to understand that she's upset/scared/worried/lonely and that she needs to feel secure, loved & understood at home - not be shouted at. I get that her behaviour is irritating, but he needs to understand why it's happening.
I would speak to her teacher (today or tomorrow if possible) to see what he's noticed & just to let him know how she's feeling.
Then I'd make time over the weekend, I'd drive to somewhere (just the two of you) that takes a good while to get to and talk to her in the car, it's a giid place as you can avoid eye contact, and they tend to open up more. Try not to 'fill in the gaps' or lead her too much, try to get her to do the talking.
Another thing to try is doing more classes/hobbies/groups out of school so she meets other kids with similar interests & in a different setting.
Plus any other friendships you can enable (not force) like friends kids/cousins etc. Even Children at school she likes but don't seem to notice her, you could see if she wants to invite them home it or do an activity if having them come home feels too worrying for her.
If she just hasn't found her groove yet, I wouldn't change schools, but if there's a good reason she's unhappy & it can't be changed, I wouldn't hesitate to move her or home school (if possible).
I hope things improve soon for her.
Ps. My friends DS was like this, but as soon as he made a friend it turned around overnight!
Best wishes.