Gosh Chim - it certainly sounds as if you've been through the mill with this guy. I can understand why you don't want to go back to the way things were when your relationship first broke down. But remember that you're a different person now and things may not necessarily pan out the way they did when you were (I imagine) struggling to cope with the end of an abusive relationship and life as a single mother.
I think you need to break this whole problem down into single issues in order to regain some control.
Firstly, your solicitor - why can't you change her? Who said you have to put in a complaint about her before you can have a different solicitor? TBH unless it's in your original client care letter, it sounds like rubbish. Contact the head of department/managing partner and say you no longer feel comfortable with your current solicitor and if they can't accommodate a move to someone with (a) more experience with dv and (b) more empathy with dv victims, then you'll find a firm who will. I second contacting Women's Aid for that reason only - they will have solicitors on their rota who specialise in this area or simply contact the Law Society for legal aid firms in this field in your area.
Secondly, social services. I think this is a bit of a lame duck actually. As you said, if it were you who was displaying erratic behaviour, drunk or high when caring for your children, they'd be in there like a shot. Unfortunately because this is a contact issue, they would expect you to step in (as the primary carer) and put a stop to it if it was not in the children's interests. I think this has a lot to do with resources - social workers have so many cases and so little time, they would find it hard to justify starting an assessment simply to advise your ex to act more appropriately when the DCs are in his care. It all takes time and money and, from their perspective, it's wasted since they can't actually take action themselves - unless of course it's against you because you allow them to see him.
His behaviour - you mentioned that you previously had a non-molestation order which you did not action when his behaviour breached the terms. Might this be where your solicitor's attitude is coming from. I'm not saying she's correct but perhaps she feels that there's little she can do to help you if, even when you get a court order to have him arrested you refuse to carry out the threat. Court orders like this are quite difficult to get nowadays especially where children are involved because the court are reluctant to set up a situation where co-parenting is scuppered in this way without really good evidence that there is potential harm to both the applicant and any children.
I think you have to draw a line in the sand and say no more. I would ask your (old/new) solicitor to write a letter as briefly as possible setting out the conditions upon which you expect contact to take place - no drinking, no drug-taking, immediate contact in the case of injury etc. Set out the consequences of breaching any of the conditions and then stick to it. If you pick up the kids and he seems drunk, tell him contact is suspended until he takes a drug/alcohol test. Stick to that line even if he takes you to court. If he gets violent, call the police immediately. Give them a statement. Co-operate with them. If he's arrested and charged with an offence, he can be bailed on condition not to contact you. If he's warned for harassment, similar conditions can be set.
You have to see this as a long-term thing. It sounds as though he's taken you to hell and back but he will continue to do so until you make a stand. All the talking and pleading in the world won't make a difference now - if he didn't take you, the police or your solicitor seriously, he won't listen to a social worker believe me.
If you don't want to be so confrontational from the outset, maybe suggest mediation so that you can draw up some sort of working agreement which involves regular testing/drug counselling as well as more supervised contact to start with. If he refuses to mediate and threatens court action, he'll get a slap on the wrist from the judge at the first hearing which is called a "mediation hearing" anyway!
Sorry if I've gone on a bit but you do sound as if you need some motivation to take the first step. Your DS's injury should be all the motivation you need. It's not good enough on his part and he needs to understand that.