I do home daycare, and have a few certain timing rules...like if not here by 8am they get no breakfast...times for lunch (like if they leave for a Dr appt, or whatever and come back, half days, etc). I have several provider friends who do NOT allow pick up or drop off during nap time (as they use their front room for older nappers and it disrupts everyone, etc).
I know many providers, so I assume centers do similar, that do not want kids arriving during "learning" or class/activity times. Its very disruptive. Perhaps in her newly moved up class there is more organized activities, etc? I would discuss with them the particulars of why.
Just because you are paying for it, etc, doesn't mean you have the right to be disruptive to the entire mornings going's on's, as some might feel. Keep the communication open and see if there is a compromise in the timing or an alternate solution?
EDIT to add~ after reading a few other replies, I just feel the need to reiterate, as I usually do on any daycare related posts. Just because you have your child in daycare...home daycare or a center (unless its a nanny who comes to your house and only cares for your child/children and you pay all of the appropriate employer taxes and benefits and compensation for a person to LIVE off of and pay a regular persons bills), you are not the boss. You do not get to make the rules. Like "Sara B" says about how they work for you. Thats just plain bull. They operate a service business. If you do not like the rules and regulations of such, go elsewhere.
Just like if you do not like how a particular Dry Cleaners does your shirts, or the hours they are open (maybe its a small place and they shut down at lunch time for an hour..they can!)...you as a consumer can look in the yellow pages and find another place to go to. Daycare is the same way. We, as providers, are running a business and you are not our employers. If you are licensed, as I am, you follow certain safety guidelines and rules set forth by your state, etc...but the business practices are for US to set and enforce. I am sorry if this sounds harsh or witchy, but so many parents here and everywhere seem to forget this point.
I pay self employment taxes (more than your regular joe-worker bee does), have none of the benefits offered that an employee who works for someone else might have access to (medical/dental, etc, etc). The perk I do get is being the boss and making my business the way I want and I happen to be very successful at it.
Ok off my soapbox.
Best of luck.