Glad to hear that your work place have been understanding of the shock and disruption of this news on your life and that you've got this week to focus on yourself and your children.
I'm so sorry that you've been betrayed like this.
His damage and destruction to your home is appalling. He's blown up his own life by cheating but then he also has the audacity to casue physical damage. What an angry baby of a man. Eww.
I mainly wanted to give my opinion about what the children should be told. The older two should definitely be made aware that there's been a betrayal and that's why he's been kicked out. If you want to give the older one more information, that's up to you but they are both old enough to know this much.
The younger one needs some honesty in an age appropriate way.
Have you read Breathless by Jennifer Niven? I didn't love it but the point is the main character (based on teh author's own experience) isn't told the truth by her parents when they split up and I think that's what makes the change even worse, she feels that she's been lied to by the parent who didn't cheat.
That he physically engaged with sex workers is a huge deal for your own physical health and to have been in the dark about that is an additional level of betrayal. I see that you're not keen to get STI checks as you're on your period at the moment but I think it's still worth while having a chat with a counsellor or someone with professional experience in this area.
With your youngest (and maybe the 14 year old), I'd also talk with their school. You don't have to mention any details at all, but let their class teacher know that there's a separation and it's in distressing circumstances. This will better help them to support your child, maybe introduce more nurture interventions, or with your older one just make you aware of some of the wellbeing support that they've got available and just keep an eye out, but also if this were a parent at our school I'd want us to signpost you to support locally.
I can see from your posts that you're obviously floored by the news but you're also concerned about the impact on your children. So getting school involved as part of a support team for them will help I think.
So, this week I'd reach out to the schools. I'd lean on your family and friends and accept all the help and love and support they're offering. Look for support and advice for you, there are options out there depending on where you're based and what you need/want at the moment, such as this:
Counselling after Infidelity or Cheating - The Spark