If you get a babysitter or casual nanny from an agency, you're more likely to get someone you can trust. They rely ont he agency for all their work, so if someone gives them a bad report, they won't get any more work, and therefore no money. So it's not worth it for them.
I used to work for a great agency in Sydney that do occasional placements, and this was exactly the kind of thing I used to do. Sometimes it was even when the mumma was sick, so she'd be home, and I'd just cook and hang out with the kids and do the washing etc. I'll give you the details via PM if you like. Maybe you could get a half day - get someone to help out in the morning, so then your mum just has him for his sleep and when he wakes up? Might be easier on her, and cheaper for you.