I'm not sure I understand why you'd have to leave him for a whole week,
including nights, with her if the primary purpose is childcare. Does she
live so far away that dropping him off with her in the morning and then
picking him up is not an option?

150 miles! 3.5 hours drive, so a week or not at all is the best option.
She might be able to come here for some of the time, but I have 6 weeks of
childcare to sort out, I might take unpaid leave from work, if that is the
only option.

Honestly, I have NEVER left any of my kids with ANYBODY for more than an
overnight and my oldest is 6.5yo. Even if they'd be fine to stay away from
me that long, I'D be utterly miserable to be separated from them for so
long. I frankly don't wouldn't consider a childcare option as remotely
feasible if it meant leaving my kids with someone, even their grandparents,
for 5 days at a stretch! And that's without even considering the
breastfeeding aspect.

that's similar to the way I feel