Biwi chahe pehli ho ya dusri, india ki ho ya japan ki ...wo apni mistakes easily accept nahin karti hai. (exceptions are there but rare !). In ur case u slapped her so u just forget that she will apologize. Your one slap has washed away all the good u did for her.
On top of it our judiciary has made such laws in favour of women that many husbands who fear false cases literally end up being a puppet in hands of the wife. Adjustment/Compromise karni padhti hai to survive in a marriage. Jo sehte hai wo shaadishuda rehte hai and rest end up in divorce.
I personally feel in ur case egos are playing a major part, see if u can forgive and forget. Even if u cant forget u can try to ignore. Is biwi se chutkara pa logey but dusri acchi hogi iski guarantee koi de sakta hai kya ????