This was a big reason we went with a center. I also like the fact that it wasn’t going to be one person looking after my child. With a single care provider, the provider doesn’t have the option of taking a break if s/he’s feeling stressed; if s/he takes a shower or goes to the bathroom, no one is watching your kid; if s/he has his own kids they will always be first priority.
My brother’s got a 9-month-old and this is what he does. My mom and the other grandma take turns watching the baby during the week. Two days she goes to other grandma’s house, and the other three days my mom goes to their house to watch her.
SIL is a teacher, like the OP’s wife, so it’s not that bad. The grandmas have the summer off, and SIL generally gets home before 5.
Don’t count on being able to watch the kid and still get work done. It’s just not feasible.
ETA: They’ve been doing this babysitting setup since the baby was about 3 months old. Before that - maternity leave.