I don't think it's a question of rewards (although I know that's the approach a lot of people take, it just wouldn't work for me) and I certainly don't think it's a question of discipline.
I think you need to accept where your child is right now - dry at nursery, and neither dry nor clean at home - and then work out how to live with that for however long it is going to be (a day? a week? a month? a year? noone can tell) without anyone being upset. For me, your situation as it stands would mean that I would pop a nappy on your daughter as she came in the door from nursery, but not put a fresh one on in the morning. And when she's ready to use the potty at home, she'll tell you
I also think (God, I'm opinionated) that the more pressure we put on our children over when they are ready to use a potty or toilet, the less likely they are to just get on with using it and with knowing for themselves when they need to go, and with not having accidents. But I know very very well that this is very hard to act upon when our children are later than the norm in being ready to come out of nappies full time.
There are also ebbings and flowings in children and how they prefer to eliminate/defecate. I've known more than one child (different families) who went through a phase of not wanting to use a potty/toilet, and asking for a nappy when they needed one, and then later on, they wanted to wear a nappy all the time because as they were becoming more and more aware of their bodies cues, they were anxious about a nappy getting to them in time (that's what one of them told her mummy in my presence), and then later on they were ready to use the toilet and of course there were no accidents because they knew exactly what was going on.
I think it's just the same as the way some children will try something out and you see them go through the whole process of trying and abjectly failing at whatever it is, and then gradually getting nearer and nearer to managing it, and other children appear to not be even starting to think about that thing (walking/jumping/talking/whatever), and then suddenly one day out of nowhere they are ready, they just preferred to work the whole thing out internally before putting it into practice.