I bought in the same neighbour as my parents bcos I've always lived in that neighbour, and I love being in the neighbourhood. The grandparents daycare thing was just a bonus and natural by-product of how things panned out.
But if I was forced to choose between (#1) buying a place that is close to my parents vs (#2) buying a place that is convenient for me, I'd probably lean towards #2 while still trying to achieve #1 as much as possible. In that sense, a 20 min drive (with light traffic) is probably getting close to my limits of sustainable travel time between my place and my parents. With a bit of traffic, that can easily balloon to 30+ min per trip, meaning you are losing an hour each day you bring the kiddo over to grannies'. And while you're doing that, you also gotta factor in your normal regular commute to and from work.
For the renovation question, I bought a place that was almost ready to move in. The reno still took more time than we had planned bcos that's how every reno (and contractors) play out. It was a huge PITA and we ended up moving back into my parents' place for something like 3 - 4 weeks. My parents were thrilled bcos they got to be with my kid every single day, and he was a cute little thing at the time. I didn't particularly liked it bcos I was just sleeping on the floor in the living room on my kid's children play mat.
Don't do what I did -- make sure you'd have a proper place to sleep in until all the renovations are done.
