We shut the door too, and she can't open it. At night it is too dark in her room for her to play (read books etc) which is why I think nights are easier than day (naps). During the day I have to make sure she is really tired when I put her to bed, and then she will usually just stay lying in bed, and go to sleep quickly. If she gets up at the start of her nap, then she sometimes doesn't go back to bed, and ends up playing the whole time.
We started the transition with night times only at first, then about 10 days later, took the cot out of the room, and put her in the bed for naps too.