Congrats, OP! Fellow SMBC here, actually about to have my second baby. Obviously you know yourself and your mum and your relationship with her best, but having been there and done that, i will say that having a newborn is HARD!! Especially by yourself. And just having someone around to do simple things while you're still physically recovering and adjusting to your new life, can be invaluable. Simply not having to think about doing the washing up, or what you're going to eat, let alone actually doing the shopping or making the meals, is so helpful. Your brain will be so occupied with all the new baby things, that having that mental load taken from you may be surprisingly valuable. And that's all if you're lucky enough to have a straightforward recovery from a vaginal birth and no postpartum depression or medical issues with your newborn. Which no-one can predict or guarantee.
So i suppose my suggestion would be that rather than setting a hard deadline for her to leave in advance, you find a way to get her to agree to leaving whenever you tell her you're ready to be by yourself. That might be 2 weeks after birth, or 1, or 5!
My mum ended up unexpectedly having to leave when my first was around 2 weeks old, and it was hard but ultimately we did fine, but i also had a lot of other support/help around. Pretty sure you don't choose the SMBC path unless you have a good amount of strength and resilience! So you know yourself and you'll be fine, just remember that post-birth is a particularly tricky time, and it's OK to allow yourself to be looked after!