Bare bones of it - what is more important to you - contact with your partner or contact with your children?
Having BEEN in a similar situation, at a similar age to you, I can verify that it is almost definitely the age of your youngest DC that is causing the issue here.
You fell pregnant within a month of your DP being released from a psychiatric unit after a breakdown, whilst he would have still been on the medication.
That DOES show poor judgement. You need to jump through every goddamn hoop SS set you to prove that you have improved your judgement.
If you do everything they ask, and you aren't putting your DC's at risk, then you should be fine.
If your SW isn't doing the referrals that she says you all need, then go above her head, IN WRITING, stating that : My Children's SW Mrs Xxx has informed me that I need to have DV counselling and my DS needs counselling, and she has failed to give me any information on those referrals. Could Mr or Mrs 'head of children's services department' please chase up these referrals and contact me (at my address) as soon as possible to inform me of the details of these referrals.
Yours Sincerely, Me.
DO NOT MENTION YOUR PARTNER'S REFERRAL!!
Then, get your partner to write a SEPARATE LETTER, SENT IN A SEPARATE ENVELOPE to the SW's next in chain of command, stating that
My children's SW Mrs Xxx has informed me that I need to attend a parenting course. I am perfectly willing to do this, but as I have informed Mrs Xxx, I am unable to attend an afternoon course due to work commitments. I am anxious to undertake this parenting course, as I am unable to live with my children, but despite Mrs Xxx stating that she will refer me to one, I have heard nothing back. I would appreciate it if you, Mr or Mrs 'Head of Children's Services Department', could please chase up this referral and inform me as soon as possible at (partner's MUM'S address) when I can expect to attend the parenting course.
Yours sincerely, partner.
You NEED to start doing EVERYTHING, EVERY SINGLE QUESTION in writing, copied in to this SW's manager, and even the head of social services in your county, AND KEEP A COPY OF EVERY LETTER FOR YOUR OWN RECORDS.
Do not ask ANYTHING without doing it in writing as well as verbally.
Create a paper trail. They don't like it, but it forces them to be far more above board.
These are the first things you need to do.