ESA = Employment Support Allowance (welfare/unemployment benefit), DWP = Department for Work and Pensions (goverment department that administers said benefit).
butterflies, you're in the UK I'm guessing?! Well done for getting a diagnosis first of all. My understanding is that's not easy here (I haven't tried!) If I'm reading your post right, you're worried about this work programme in case this angry alter comes out and makes things difficult? Or you're worried they'll try to get you into work when you're not ready? Or both

Do you have much communication with this alter? Could you come to some kind of agreement with her about when she can be out/what is appropriate behaviour? Could you offer her some alternatives to express herself (writing, drawing, smashing things, I don't know)? Her saying horrible things to your kids is not ideal, either
About the work thing, can your therapist write something explaining the situation, to back you up in case you need it? Or could you go to a benefits advice centre, maybe get some support or advocacy around this situation?
Anyway, welcome, and I hope things settle down for you
DX: DID. Host - 'Owl', Gemma (16), Jake (14), Jessie (12), Abi (7) Kit (5), Lamb (8)