Hi there
It sounds like you and your brother sometimes don't get on, which is quite normal, but it does sound like sometimes it makes things difficult at home. This can mean that your mum gets angry with you and your brother a lot.
You told me about how your mum smacked you round the face and then how she threw you onto the bed. It sounds like this was really scary for you - especially when she then threatened to punch you. What your mum has done here is not okay - it's never alright for an adult to hit a child, no matter what's happened.
Your mum has then gone on to tell you that she wouldn't miss you if you went into care - this is wrong for her to say as well.
You asked if smacking or threatening someone is abuse and yes, both of them are. Physically is not the only way that someone can hurt you. Telling you that she wouldn't miss you if you were gone is another form of abuse. You can find more information about different types of abuse in the Explore section; Physical abuse, Emotional abuse, Sexual abuse and Neglect.
It sounds like you want someone to talk to about what's been happening at home. You are right in that if you talked to a teacher at school they would want to keep you safe and so would probably need to tell someone. Even though what your mum is doing is wrong, ChildLine thinks it's important that you make the decision about what happens next.
Talking to a ChildLine counsellor could be a good way of finding out what your options are, or even just to get things off your chest. Have a read of the ChildLine confidentiality policy. What you say is between you and ChildLine, unless they are very worried about your safety or the safety of others, then they will talk to you about whether other people need to know.
I'm really glad that you sent me this letter as it could be the first step towards things being better at home.
Take care
Sam