As an adult, it took me 6 years to get over my mother's death properly.
So, for someone to lose their mother as a child, especially as a very small child, I think that would absolutely count as a fundamental and totally life-changing/life-shaping event. Especially if she lost her mother before she was 3, as it will be part of her formative experience of life.
I do think, from your post that you are underestimating the effect her mother's death will have had on the child.
So, this is a long-term and serious thing. There is no way this can cause no effect or be over quickly.
Whilst I think therapy could have/could be very helpful for her, so will having a very stable, unconditionally loving presence in her life. In fact, in terms of forming stable attachments on a life-long basis, it's probably absolutely the most important thing that can be done for her long term welfare. And it looks like that is what her father is trying to do. I think he can only be commended for that. Looks like he is trying to show her that he is fundamentally there for her, no matter what.
I think long-term, she will stabilize as she gets through her grieving and healing. Whilst being a staunch disciplinarian in these circumstances is fraught with potential to damage her ability to form secure attachments to people. But it is long-term, and there are no magic wands to be waved here.
I am sorry that this is grueling for you. It must be hard. It he is a man who is putting his child first, and, especially in the circumstances, I think that needs to be respected.
So, I do think it sounds like your relationship isn't viable. Not because of the distressed child, or as a result of your partner's behaviour. But because, fundamentally your outlook, and therefore your priorities, are too different.
Often that can be surmounted by alignment of practical actions, a shared view on how to live life. There are exceptional circumstances here though, which make that alignment difficult. So I think you need to either radically alter your outlook, and accept that he does know best re his child, or you need to part.