So I am right in thinking that you are a) being charged with 3 counts of ABH and b) the only action you took was a push (what do THEY say you did)?
It's impossible to say precisely what your sentence will be. I don't even know if ABH will stand up (ABH has to be actual bodily harm, so a push that results in no injury would be a common assault - ABH is injury sensitive. Often they are "over charged" at police station stage but prosecuted as common).
I suspect that the Magistrates would accept jurisdiction so the maximum sentence imposed would be 6 months. For a first time offender pleading guilty at the earliest opportunity you will be entitled to a 1/3rd discount.
The Magistrates Court Sentencing Guidelines indicates for a first time offender pleading not guilty, the range is low level community up to 26 weeks custody. The entry point is high level community. But that is on the basis of no permanent or lasting injury caused.
In your favour is the fact that it was a first offence, not premeditated and there was an element of provocation (this is not a defence, but mitigation). Aggravating is the fact that it was while you were in drink, it was domestic violence and you did it THREE times!
It is impossible to advise fully without seeing all the statements though. Best advice I can give you is get to see a solicitor IMMEDIATELY. Answer no further questions to the police unless you have a solicitor present and take his or her advice - there is lots a solicitor can do for you, including advising on evidence, plea, mitigation, negotiating a plea with CPS and advising on sentence.