You wife probably can't tell you exactly why she doesn't want family.
She is a very sensible woman.
With family you feel 'beholden' to them, i am still being reminded 16yrs on how MIL 'sacrificed' her own time to care for DS for 5months whilst i went to work. This is despite the fact we could afford nursery at the time, but she was begging (as your lot are) to have him.
Like another posters said, Mums/MIL tend to argue or not listen when given instructions on how to care for the DD. They can be quick to remind you, 'Your DH was raised that way and he's turned out alright'.
With nursery there are no strings attached. Its simply a contract. You pay them, they do as told (in most cases). When you want to stop care, you simply give notice and walk away. Parents will be in the child's life a long time, sometimes changing care patterns can be difficult to change once they are used to a particular routine and stopping care with GP can be fraught with problems, emotional ones.
Your DW has the challenge of also pleasing two parents. If she goes to one and not the other problems, if she splits care it becomes more cumbersome for her as both grannies i guarantee you will have different views, preferences etc.
The advantage of using parents are that you save money and that DD is with someone who loves her. But there are lots of cons too. With nursery she's not with people who love her, but in a safe environment all the same and she will be happy and get to mix with other children her age, make friends etc.
Your DW may also not want that amount of contact time personally with the parents, it can be stifling especially when you add childcare to it. with nursery she make a quick phone call, quick hello and good bye without having to explain herself all the time.
No doubt, there's a lot to think about.