Wow, you have 4 kids and you're doing it alone?? Honestly I also have 4 and a partner and I have nearly lost my mind. It is SO full on.
I was feeling low a few months back, like all I did was chores and parenting constantly -never any of it as well as I wanted to- and it's too much to never have time alone, I don't think people realise. Everything you do is juggling at least 2/3/4/5 jobs at once and each of those jobs is ALWAYS interrupted.
I think my youngest was a similar age to yours when I felt very depressed, (history of PND-) but she's older now and honestly it does get easier. (Especially when the sleep improves.) I also contacted my Health Visitor and she was amazing! Put me forward for a group for mothers with anxiety which was actually helpful, but even better, I met a friend there who has changed my life actually. I'm in a much much better place now.
Can you insist your ex takes your daughter the same time as your other kids are away?? I honestly think you desperately need some time alone.
Very much in awe of what you're doing, I've been finding it SUPER hard and that's with a partner. Sorry your friends have been shitty, time to find new ones. I think the single parents groups on Facebook might be worth a look.
Hang on in there! Sending ♥️ and 💪