MIL is deaf without her hearing aids so I have always been concerned about her having DD1 overnight. However when I was having DD2 MIL stayed to look after DD1. DD1 would get up and wake her Nanna if she needed anything and they were fine - and this was 5 nights in a row! DD1 was just 3 at the time too. You might be surprised how your DD copes with your mum especially as she sees her a couple of times a week - they probably have their relationship pretty sorted by now.