The fact that you didn't like the food but ate it anyway could mean that you feel you do things to please other people, even though you don't want to do them.
I think the psychotic girl in your dream is a part of you that you aren't happpy or comfortable with, your
shadow.
Since she attacks your family after you were dissatisfied with their food, she could represent the part of you that isn't afraid to speak up and complain about or question things.
The girl wanting to hurt your cat - who is calm and makes you feel relaxed- could mean that you are afraid that if you express yourself more and don't always do what everyone says your life will be less calm and you won't be able to relax so much.
The weather in a dream often has to do with your emotions - snow could mean that you are feeling "numb".