YABU, sorry. Your FIL has a right to his opinion, and I agree with him.
The best place for a child of that age is with her parent, someone who loves her, and thinks she is the most special thing on this earth, surely.
My DD is 15months, has never spent a day away from us, and that is how I think it should be for her until she is three and starts playgroup (which will be for her benefit, and NOT mine).
You say you don't NEED to work, well sorry, I just don't get it? A 13month old is a BABY. She can't tell you if people are being unkind to her, how can you say she is happy???? you can't possibly know.
If I was in a position where I HAD to use childcare, then it would tear me apart having to leave my DD for that amount of time, 3 days a week. I could never be happy with that decision.
When my DD has her nap, I want her to be in her own quite room. When she has her lunch, I want to chat to her, help her and let her take her time. I want to play with her because I want to, not because I'm being paid to.
Even that you felt you had to mention that you have breakfast and dinner together baffles me. Of course she should be having her meals with you, ALL her meals. You are her Mum.
I don't think this has anything to do with how important your career is, or how it's just as valid as your Dhs career...............HELLO!!! this is your baby Daughter we are talking about, right? Don't HER needs come first AT ALL TIMES?
Children are little for such a short time, and need to be nurtured through those first few all important years by someone who loves them, and truly cares about their feelings, needs and development. Not by people who are being paid to do a job.
Sorry this is harsh, but you said you didn't need to work, and there are so many Mums out there that HAVE to leave their kids in childcare, and would give anything to be with them, so that is why YABVU IMO.