As Longtallsally has said, going to a refuge isn't just about having a roof over your head, its also about being safe and getting support from people who understand what you are going through. They will have or be able to point you towards resources to help the children get through this too.
If you have money then you will be able to pay them rent so that you don't feel like you are taking advantage (if you don't have money they will help you access housing benefit).
Certainly give them a phone and tell them everything, they will be able to give you advice.
Having some official record of ex's abuse will help when it comes to restricting his access to the children and receiving legal aid for the divorce if you need it.
Well done for getting out. I don't know how old your children are or who is paying for their private education, but their safety and wellbeing is much more important than a short term disruption to their education - though obviously if they are sitting exams this summer then getting them resettled quickly is important.
I presume the notice period for their school is about school fees, and does not actually stop you moving them elsewhere if you need to for their safety and well being (and needing to move/go into a refuge to escape an abusive home situation would count!). The fees will need to be paid whether they attend or not but (speak to a soliciter) arrangements to pay this could be out of the marital assets as part of the divorce.