For a moment lets reverse this situation. Say it was you (a male) that slapped her. Then if the police were involved you could be taken to court and had a criminal charge on your record. You might also have issues trying to have access to your child.
I was in an emotional and physical abusive relationship for 7 years out of the 10 we were together. The same, got slapped around when she was drunk. No matter what I did I could not control her from that abuse. In hindsight now, I should have got the police involved.
If you report her abuse to the police at least you have a record of such illegal action in case you have to leave the relationship and file for some level of custody. A first visit free family solicitor might be worth your time. Covert recording of any incident might also be to your benefit. Evidence is handy.
Also- if she refuses to attend a psychologist I'd make an appointment with a family counselor. Invite her to go along. If she refuses then leave it at that and attend yourself, after all you need to learn more about how to cope with her abuse right? After your meeting she might ask you how it went...say "its confidential but you are more than welcome to go with me to the next meeting". If she asks why you are going - "I'm learning how to tolerate abuse". End of conversation.
I too had my then partner say (when asked why she hit me) "you made me do it" and "your bipolar forced my hand". How silly. My now wife of 10 years laughs at that and has never struck me.
Finally, upon hearing her for hours arguing, there has to be closure. The silent treatment is a form of abuse also therefore I wouldnt advise it. Better to select your words carefully like "I've already answered that / we've already discussed that"... "how about we got for a walk with the dog"?
In the following thread there is a technique whereby you can make a pact for closure. It has worked for us every time. But you both need to agree on the concept. It's a matter of space, respect, time gap and conditions.