Okay. I'm concerned because - you say he is seeking help and going on this course, so I'm guessing that you have hope he can change. I can see why you would hope that. The course exists, so some men must change as a result of it, this is true. However, it's a big ask, a really really big ask to expect someone to change their entire way of thinking and being. OP, you are a kind and caring person, I can tell that from your posts. Now imagine you were suddenly told "There is no place for kind and caring people in this society. You must become ruthless, selfish and hardened to violence" and then put on a course to try and learn this. I'd imagine that however much you wanted to fit into this new society, you would find this really hard, perhaps impossible.
It is possible for abusers to change, but more often than not they don't, unfortunately. There is a great book often recommended on Mumsnet called "Why Does He Do That?", it is written by a man who runs abuser programs. He has seen hundreds, maybe thousands of men come through them. The programme is their best hope of changing, but sadly, a lot of them don't make it, and one of the interesting things in the book is where he says that there are clear signs from the start as to which men are likely to come out with a new outlook, and which are likely to carry on as usual. Be warned, some men even get worse.
One of the biggest indicators about whether a man is going to change or not is for him to recognise his behaviour as wrong. Your DP isn't - in fact, since he's agreed to go on this course, he hasn't made any kind of effort to reign in his abusive nature at all, which is worrying. Just from this thread, since he's signed up for the course he's done the following:
Exerted control over who you see (insisting he will "choose" you a buddy)
Acting as though he gets to say what you're allowed to do ("allowing" you to do counselling as long as you fulfil his wishes re the buddy)
You cannot trust him to look after DD while you do this course
He continues to not acknowledge her existence
He grills you on what you've been talking about when you see friends (it's very likely he's expecting to be able to grill you on what you talk about in counselling, which will make it difficult for you to be honest with the counsellor)
Restricts your movement in ways such as preventing you from taking out money
He is gaslighting you ("Remembering things differently" - it is conscious and designed to make you think you are going mad)
You do not feel comfortable telling him you have access to help such as freedom programme or CBT
Puts you down and calls you "useless" (you most certainly aren't!)
Is expecting you to give up your baby groups, swimming etc in order for him to afford counselling, rather than making sacrifices himself
Telling you what to do with the "undermining" thing
This is the most chilling IMO - He has TAKEN your baby daughter, who you do not trust him with, solely in order to frighten and intimidate you into obeying him. She was screaming and unhappy and he didn't bring her back. He didn't care. His ONLY interest here was to frighten you.
The ONLY way you can keep your DD safe from him is to get both of you away from him. I am frightened for you. You said earlier in the thread that he doesn't "fit" into any one category of abuse - do you realise that even one item in those lists means that he fits that category - it would be extremely rare/unlikely for any one person to fit every single behaviour associated with physical, emotional or financial abuse. The fact he has traits spread over all of them is worrying.
He can still go and do his course - you can still go and do yours. If on the offchance it makes him into a wonderful, doting, caring father, you can always get back together. But after what he's done today, I don't see that he deserves to be given a chance while you stay with him. You cannot possibly watch DD 24/7. What might he do, in the name of keeping you in line? Once he's taken her a couple of times and you no longer panic because he always brings her back - then what?