I agree with the others. It's always easier when baby is in comfortable and fimiliar surroundings. Plus everything is already baby proofed and ready to go.
At the end of the day though I wouldn't stress. Babies adapt really quickly and it's not like it's a total stranger it's your Mum. She's a pro at this baby thing so give her some credit

She raised you so even if he's upset at first she'll know how best to distract him. I used to always stress when others would watch my kids but everytime I'd come home I'd be almost disapointed to find they had cried when I walked out but then stopped 2mins later and forgot about me