I think are you doing the absolute right thing. My son was/is very quiet around others. Whether it be kids or adults.
We did the mommy and me classes until he was 3. And at 3 he started going to the same place, just for an independent class. I wait in the lobby with him and the other kids and parents until the door to the class opens. I say a quick goodbye and that I WILL BE BACK. And the teacher leads him into the gym. The first few weeks were hard. Now, he LOVES it. He is the first kid in and the last kid out.
Independent classes are great places for kids to work on their social skills.
For the first few weeks he played by himself. And then along side other kids. And now WITH other kids. Its amazing.
And I know that if I continued go to classes with him, he would have just hovered around me and wouldnt have make as much progress as he has.
I think its great that the pre-school is open to having you stay until your child is comfortable. But, he may never be comfortable with you there because he knows any second you may be leaving. And prolonging it will only make it harder.
I was lucky that the teacher insisted, I kiss and walk away. And my son knows the routine. I say good-bye, he has fun, I come back.
BUT, you know your child better than anyone. What worked for us, may not work for you and your family. Best of Luck!!!!!!!!