You sound like a model client. I would have no problem with your child coming in the morning and then leaving at/after lunch. I would not allow a lunch time drop off as it would be difficult to get the child into the afternoon routine (tried and tested) so I would then say bring for the day.
This is your day, it is paid for, so like the other posters have said, it is none of our business what you do when your child is here as long as no policies are broken.