OP do not send this text. It is unprofessional, poorly written, and could be used in evidence against you.
First - your nanny is presumably an employee (otherwise you couldn’t sack her). You need to follow employment law and should get advice from an appropriate source BEFORE you do anything.
If you do not feel it is safe to leave your children in her care - don’t. But sacking her or disciplining her is separate.
It is my expectation (but I’m no expert in your laws) that the fact she is live in complicates things more. Sacking her also makes her homeless, and I would expect there are laws around that in terms of notice, compensation etc.
Second - she did not leave your child with a random stranger. She left the child with her partner, who at your invitation lives with you all. YOU invited him into your home. You can argue that he isn’t meant to enter the house during specific hours all you like - but unless that caravan is equipped as a separate residence I’d expect the interpretation would be that he is your guest in your home. I live in a different country - but if I let someone stay in a caravan in my yard - and I’m not setting things up as a commercial rental - then they are my guests.
The fact that he is her partner doesn’t mean he is safe. But then you have no more or less reason to see him as safe as any other person (including your own husband, step children, friends , family, etc). By inviting him into your home you accepted that he could pose a risk - just like the nanny you hired, your friends and family etc.
Even if he wasn’t to enter the house, and didn’t, you invited him in to your family. If this was some grand scheme to access children for abuse (homelessness is really common where I live, seems weird to think it could be a multi-step predatory scheme rather than just reality of our economy) - and 5 minutes (or even 15 or 20) unsupervised was what he was looking for - he’s had that every time your nanny goes to the toilet, or takes a shower after Bub vimits or s on her, or leaves one child in one room while attending to the other in another room. Because he’s on the premises, and the children see him as safe (cause you invited him to live there! And he’s family to their nanny!)
If you no longer trust your nanny then part ways. But you need to give appropriate notice, and appropriate financial compensation according to local employment laws / your contract.
Living at work brings many challenges, and six years is a long time to live at work. It’s genuinely impossible to maintain proper work/life boundaries when you live at your work full time. My experience is that employers are often perfectly fine taking the advantages of that - but things go poorly when they aren’t willing to take the disadvantages of that - and a major disadvantage of having your staff live permanently at work is that they simply cannot keep their personal lives out of the workplace!
A revolving door of shorter term live in nannies is probably your best bet if you don’t want people to start blending personal and professional too much.