Hi OP
I came onto Mumsnet to frantically look for ideas to deal with my situation and nearly straight away saw your post. In many ways your DD2 sounds like my DD1, aged 12. I have two other younger DD, who are sweet, well behaved and are terrified of her. DD1 routinely steals their stuff and lies very convincingly about it. If they have sweets she'll hunt them down and eat them. I love her to pieces but our home is hellish as it's full of tension and dread, waiting for the next explosion or meltdown.
We first tried to access help when she was 7 or 8 and like you got told our parenting was too lax. However, whenever we try to get her to do anything - and I mean ANYTHING, such as putting her empty yoghurt pot in the bin - it turns into a fully fledged meltdown and often ends with my other two DD crying in fear. Last week she punched me and I think now she's crossed that line it'll happen again. I've told her that if she hits me again, I'll call the police. She pretty much has the body and strength of a grown woman, but the emotional control of a six year old.
I've been told I need to do a parenting course and like you I bloody resent the implication that my parenting is at fault. I'm self employed and can't take time out in the day but I'm going to have to find a way. I'm hoping I might learn something about how to deal with her. We had one appointment with a child psychologist and they said, "Yeah, she seems to fit ASD, but we can't tell from one appointment and the road to a diagnosis is really long and hard and probably not worth it" then they discharged her with no follow up and suggested I do a parenting course. I'm waiting for the letter offering it to come through.
I'm at home today because after the most recent meltdown last night/this morning it took me until 11.30 to get her to school and now I'm too upset to be able to go to work. I think I will have to phone social services this afternoon, once I find a way to stop crying.
Anyway, although my post is of absolutely no help to you whatsoever, I wanted to thank you because your post made me feel less alone even though I wouldn't wish this shit on anyone so I'm sorry you're going through it. I also wanted to say, you don't sound like a bad mum. You sound like a desperate mum. You sound like me. :(