He snaps at the slightest thing, then tells me all I want to do is argue!

[mmmmmmmmno]

Just as the title says really. DH has a really short temper, I’m so fed up of this. He has just been swearing at me in front of DC

Abusive behavior

Have you read Lundy Bancroft's Why Does He Do That?

Im guessing the answer is partly at least that you have been trained to adk for very little and to rarely challenge him.

Because all he wants to do is argue. In order to 'win'. And to win, he has to create a loser.

Its abusive op and I'm sure you know this.
See about getting out. No child should be in an environment where their mother is berated constantly by their father.

Yes, and also, having the power to upset you makes him feel powerful (briefly)

Oh I know this situation! I went through this too.
The only thing I can say is if you don't want to break up, he must now acknowledge his short temper and seek some help.
If he doesn't seek help it will just stay in this cycle.

Tell him to fuck off and get rid of him. He's a twat.

He's verbally and emotionally abusive and is gaslighting you by saying you are overreacting

Some men need to be binned.
Your 'DH' is evidently a prime candidate.