Feeling's are allowed... And sometimes feelings make us do wierd things but thats okay! Pushing your mum maybe wasn't the best idea but that was your way of expressing how you felt in that moment... That's in the past now, there's nothing you can do but tell her you knew it was wrong and try and learn from this experience and somehow differently control how you feel...
Leave the situation and go for a walk?
Or scream into your pillow?
Take a look at the distractions list... I believe some could be used in the same scenario if it occurs again.
Although this would dealing with your emotions, the important thing would be to avoid this happening again. As Facet has said... A family session is one option? You could possibly write her a note and tell her how you feel? Or, try asking for her help to solve these issues?
Police and being locked up honestly wouldn't help. How are you expecting yourself how to learn a different way of dealing with these emotions if you have no way of feeling them?
Don't be too hard on yourself. Feelings and emotions are allowed, in turn our actions and reactions vary.
Stay strong, Kia <3