Committing an offence while drunk always makes matters far WORSE in the view of a court, so trying to use drunkenness as a defence is pure madness.
Being found guilty after pleading 'Not guilty' adds 50% onto a custodial sentence (and makes the severity of non-custodial sentences greater too).
You've got no valid defence, so why make things worse for yourself? PLEAD GUILTY!
When sentencing a 'Section 20' offence, a judge has to consider both 'harm' and 'culpability'. Going to a person's home to assault them (and doing so in front of their children) almost certainly places 'culpability' in the 'high' category. The level of injuries sustained by the victim (plus the psychological trauma to the children) means that 'harm' is also likely to be assessed as 'high'. So it will seen as a 'Category 1' offence.
The 'starting point' sentence for a Category 1 Section 20 offence is one of 3 years imprisonment. The minimum sentence that can be passed is 2½ years imprisonment, with a maximum of 4 years. However those sentences apply to an offender who is convicted after a trial. An early 'not guilty' plea can see a reduction of one third in sentencing.
So, face up to it. You ARE going to prison. You can either plead 'not guilty' and get sentenced to 3 years (meaning that you'd actually be 'banged up' for 18 months) or plead 'guilty' and get sentenced to 2 years (meaning that you'd serve 12 months). [Sentencing for the Section 39 offence is probably irrelevant anyway, as it's likely that the sentences would be served concurrently anyway].