I remember both me and my partner being in tears with exhaustion on day 4 and my mum walking in, picking up baby and somehow instantly settling him.
I had this too with my MIL. I think it's because both me and H had the mindset of "the baby is crying, OH NO THE BABY IS CRYING, I don't know why he's crying, what if I can't stop him crying, I AM A TERRIBLE PARENT". Whereas my MIL came in with the attitude, "The baby is crying, he obviously needs something, I will give him a cuddle and try some things until I find out what he needs". It was just way less fraught for her because she was one step removed and had confidence that she would figure out what the baby needed. That was actually very reassuring and calming for me.
OP - as a PP said, only you know your mum and whether she might actually be able to take care of YOU and give you a break, or whether she will simply stress you out more. If you know it's the latter, then do stand firm - although PPs are right that help can be a godsend, maybe your mum is not the person to provide that help. If you have money, you can even throw some of it at paying someone to be that help if needed.
Also, the PP who wheeled out the old "your mother will DIE SOME DAY" - seriously?? The fact that all mums will die some day doesn't mean that some mums aren't stressful and unhelpful, and that all mums can therefore do what they like when their daughters are exhausted and vulnerable.