Fanta, it is not wrong of you not to tolerate this treatment of your daughter.
There are usually a few posters around who suffered abuse as children, and have reported before feeling angry with their mothers for allowing it.
It all sounds very wrong to me. But you always get dismissive posters, particularly over one incident.
It is not uncommon for threads to start as little things, with mostly dismissive posters, and turn out to be about very serious abuse.
You have had here people changing their opinion when you mentioned the other incidents.
You have been in a difficult position of having OH's word against your DD's.
In this case you have heard what he said, and he has admitted to smacking and you can start from there.
Was the smacking on the face?
I think you need to start believing your DD and let her know that she can tell you anything that happens. And reassure her that such threats are not real.
Most children worship their parents and wouldn't make lies like these, particularly to the other parent.
And I think you should put your foot down with your OH. This should be the very last time he makes such threats.
People were surprised about the smacking versus the threats, but emotional abuse can be worse than physical abuse. If your daughter believes he will carry out such outlandish threats, it is not good at all.
But the smacking, even if bottoms, can lead to more serious abuse if he is like this with her. And because he lies about it.
A responsible parent wouldn't lie about it.
I wouldn't trust him either.