I don't really have any advice for you, sorry. My DS was much the same. His day sleeps began to get better around 15-16 months, while his night sleep improved after about 18 months. Since he was around 2 he's been mostly putting himself to sleep and very often sleeps through the night.
We had no routine till he was nearly 2, just couldn't be done. I'm just telling you this to give you some hope
For daycare, try not to stress about it. Despite all our issues with sleep, it always seemed to work out ok