FlatsInDagenham -
This is about respect and value. Hitting someone shows a lack of respect and empathy towards another human being. A sense of entitlement and ownership. A child is not a possession - he/she is a human being in their own right. This is assault. I can't believe that he thinks it's OK to assault another human being. Completely unacceptable.
Bad people aren't one dimensional characters. My father is otherwise a very nice, good person. He is capable of acts of huge generosity, care, love and compassion. Still, when I was 5 he hit me with a belt across the face. It started off with slaps with his hand across the face, before escalating to harder hits, then belts. When he lost his temper he hit my mother, my sisters, myself, the wall - whatever was available to him.
Somewhere deep down he thought that was an acceptable reaction when he was stressed or his authority / judgement brought into question. It only stopped until I learnt to fight back, at which point I was 15 - doing terribly at school and severe self esteem issues.
Being slapped as a child is painful, humiliating and deeply damaging to your self worth and confidence. It's not just a simple tap when losing temper. It's soul destroying.
Warning signs should be going off now that even after cooling down your husband sees no problem in disciplining your child this way.
This about respect, value and authority in your relationship. He knows you don't agree with him treating your child this way, yet he continues to do so. He doesn't value your opinion otherwise he would stop. Even now, he refuses to see that slapping a defenceless child or anyone for that matter is completely unacceptable.
Not to mention disagreements over alcohol ... You should be working together as a team, making joint decisions on how best to discipline, motivate, develop your children.
As for devastating your children if you separated - kids are strong, vulnerable but incredibly resilient. They will learn how to cope and you will be able to support them in the best way you can. They will remember what's happening, they will pick up the tension between you - all the said and unsaid disagreements.
In all likelihood, staying would be more damaging. It is no coincidence that my grandmother, mother and myself have all been in emotionally and physically abusive relationships. Imagine if one of them had walked away sooner - how much damage could have been prevented.
A father figure is probably the most important figure in your daughters life. You both are the reference point for how men and women should act in relationships, how they should communicate with each other, what love means, what respect means - and not just now, but for the rest of their lives. This is a huge responsibility. It involves making emotionally tough, but unselfish decisions as to what is the best interest for your children - for now and in the long term.
You haven't over reacted. You've done the right thing. Please, please walk away now. There is no excuse to hit a child, ever.