Can you find some help? You are incredibly important to your children, and you need to help yourself feel better for their sakes if you can't do it for your own.
It is absolutely awful to see your children suffer, and bullying is just terrible to deal with. Have you gone to the school again for your daughter, and then followed up on your visit? Could the police get involved? Is there someone you haven't yet talked to at the school? (Head, deputy head, head of year, councillor, form tutor, specially nice teacher, parent governor, person in charge of pastoral care, matron.) Is there someone who can go with you?
I'm so sorry about your cat; of course she is important. My cats are the light of my life, and lots of people feel the same. Death is painful, whether it's a cat or a person.
You are going through an awful time right now. Please get some help: doctor, friends, family, crisis lines. Hang in there.