Scared to be their mum...

Please no nasty comments as I'm already feeling very broken.
I Have just found myself to be the most imperfect mum.
I am a SAHM with a partner who is always away for work and my children's father only in their life when he feels like it.
I don't smack my children but I do sometimes yell but nothing compared to what I've just done.
My children 11 and 7, oldest being a girl and youngest a boy pushed me to the point I scared myself.
They were in my room on my bed playing around when I heard screaming and fighting, I immediately called them out and asked the problem, my youngest replied with "she was pointing a light straight in my eye" I asked my daughter and she said she didn't, I then asked my son again what happened and he repeated his previous story, again my daughter denied it. At this point I started getting angry that someone was obviously lying. My voice became louder and they started fighting with each other calling the other a liar. At this point (which is where I start breaking both their heart and mine) pushed them both against a wall and started yelling at them to tell me the truth. I never hit them or squeezed them or physically hurt them but the look on their faces showed me I was hurting them emotionally and scaring them both. At this point I was shaking and turned around and punched the wall behind me (not near the kids). I then sent them both to bed and slammed their doors on them.
I then sat down and cried so badly, I calmed down and retrieved my children from their rooms. I cried why I was apologising to them and told them I loved them and why I got so angry and kissed them and hugged them but the looks on their faces showed me I had scared them so much. My children gift constantly and I never find out the truth about what has happened when asked so why did I loose my temper so much tonight??
I hate myself for loosing my temper the way I did, I've never done that before. How do I make this right???