I am a bit confused about your situation, as in the OP you say
I totally get it if you are a single parent as I was one for 10 years.
So, from this, and subsequent posts I get the impression you have a partner, and are no longer a single parent ?
Also, that you presumably have a much older child, or children ?
So might they not be able to babysit for the odd couple of hours ?
I’m now in a situation where I have no family support whatsoever.
and then later you say
We have tried many sleepovers and just daytime visits but she freaks out. She always wants to come home , so it sounds as if you do have family support and a willing sitter.
I mean, I wouldn't expect an older Grandparent to have them overnight, but you are talking about never getting a break EVER, in your title, and it doesn't sound as if that is the case as you read through your posts.
I read "never getting a break" to mean you literally have no-one who will have them whilst you go for a hospital appointment or a smear or to get a hair cut or a filling at the dentist or to go to a funeral or a job interview where you can't really take them. It doesn't sound as if that is the situation you are in?