It seems you're prompted to ask for advice, after 3yrs of this behaviour, because it's getting worse. And that's worrying. As others have said, this is abuse even if it's not physical. You are being harmed - as is, importantly, your daughter.
For the moment, be practical (put the emotions around your relationship with your partner somewhere to be processed when you have the time and strength to deal with them). Compile a list of dates, times, what was said and how you felt (particularly safety wise) as best you can from memory. Start keeping a diary from now on. Promise yourself you'll call the police the next time - or, if your list feels bad to you once you've written it, go and ask to speak with the station DV lead. Call Women's Aid, this week and tell them all. Start pulling together birth certificates and other ID, information about finances etc etc. Put this where you can get hold of it without problems - keep it, and the diary, at work? Start checking out your legal rights when separated (WA can help with this?) And you do have to separate, for now at least. Neither you nor your daughter can carry on living like this.
The onslaught of grief after the death of a parent brings out the worst in some people. So does heavy drinking - and there is a very clear link between heavy drinking and domestic violence, including psychological. You have the advantage of knowing the good as well as bad parts of your partner's personality. But the truth is, that "good" man has gone for the time being and won't come back, if at all, unless your partner acknowledges his behaviour and its causes and decides to get help.
Getting counselling together will only work after he's taken this first step for himself. And he may never do so. The threat of fighting for custody is just that. Good luck to him arguing in the Family Court that the best way to raise a small child is in the pub every night, followed by a session of drunken ranting to loud music. He doesn't want custody - he wants to scare and belittle you, because that's far easier than being honest about his drinking and appalling behaviour.
I was struck by your saying you have few/no local sources of help. But help can come from the most unlikely places, once you ask for it. Start with Women's Aid. Speak in confidence with your work HR department or a trusted colleague. See if there are local single parent groups you can talk to. And think about getting counselling for yourself, so that you are able to see your life from a different perspective, and so see more clearly how you want to change it and how best to do so.
I wish you the best of luck.