Broken family

So, are you over 18?

Then you can do whatever the hell you want to (so long as it's legal). This does not mean your mother won't complain. If you depend on her for a roof over your head, that could be problematic. So try not to be dependent, or don't take obvious action (you can email your sister and your mother never has to know this) until you're no longer dependent.

If you're under 18 then the same advice applies except you wait until you're 18.

By the way, you may be wrong about them 'hating' each other.