I've heard about other momma buns getting upset/sad when separated from their babies, so yes it can happen. If her babies aren't in a cage or pen next to hers, you could try that. It can sometimes help for them to be right next to each other. I also let my momma bun have play time with her babies after I had to separate for weaning. You just have to keep a close eye on them to make sure they don't start to irritate momma trying to start nursing again, or if any hormonal behavior starts up. And when the babies are 10-12 weeks old you won't be able to let the boy buns play with momma or sisters anymore, so you don't end up with a pregnancy. Unless playtime together is what you are already doing and it's not working.
With her not eating hay well, have you decreased her pellet amounts back down now that she is no longer nursing? If not I would try that and see if it gets her eating her hay again. If you already decreased her pellets and she's not being fed too many that she is just filling up on them, then the lack of hay eating could have to do with being separated from her babies. If so then rearranging things so they are in pens next to each other and letting them have playtime should help. If those changes don't help her and you still feel like she is upset about being separated, the only other thing I might try is putting one of her daughters back in with her so the separation can be more gradual, then after a week or two try separating the daughter again.
The other thing you need to check is that by suddenly weaning all of her babies at the same time, she could have developed mastitis. So you'll need to check her belly and make sure none of her nipples are inflamed or hard. if she does have mastitis, you'll need to get her to the vet right away.