My mum looked after my twins for 10 months when I went back to work after my maternity leave. I agree with other posters that in lots of ways, you forfeit the right to dictate every last detail - if you trust your relatives to provide good care for your DD, then you have to trust their judgment bite your tongue. I was quite obsessive about sticking to the routine, and giving them only the food I'd left out, which groups / toddler sessions I wanted them to attend which with the benefit of hindsight, was slightly OTT and led to a little bit of tension.
I'd start with agreeing a set day (or even a set pattern) for each couple so that everyone - your parents / ILs / DD and you and your H know what's happening and can make arrangements accordingly.
I suggest you agree up front the financial implications of it - if your parents/ILs are going to be out of pocket for anything (paying for toddler sessions / travel / petrol etc) are you going to pay for that?
Similarly if they want to have a week off / go away etc how are you going to handle that? Do you need notice (i.e. if you want to get an extra day at nursery sorted out?)
Similarly have the conversation about what happens in emergencies (say DD is not well, or the ILs aren't well, or she gets sent home from nursery) - they might feel put upon if they think they're at your beck and call for other days too.
Are they looking after her at their house or yours? Perhaps sort out an extra buggy / car seat etc / toys for them to have at their house if its going to be there? Agree how you're going to do drop off and collection. Depending on your job, be there when you say you will and don't be late. I think in lots of ways you have to treat them as if it were a nanny - you shouldn't take advantage just because they're your parents or ILs (I did cause a big row once when I went out with clients and kind of expected my Mum to put them to bed without me asking).
It really helped with us having an end date - we decided they would go to nursery at 2yrs old, and everyone worked to that timeframe. If you do think you'll want her to attend playgroup / nursery for more days etc as she gets older, mention it now so that they don't think they're being "sacked" so to speak if and when that time comes.
And the over-riding principle - you must act like they're doing you the biggest favour in the world (which they are really). Be understanding, they're giving up their precious time.