J.H.
I have five children. My oldest is eleven and my youngest are 4 year-old twins. They have all gone through clingy stages. My six year-old though has always been more clingy than the others. So part of it may be a stage and part of it may be her personality. When my twins were born, I think my daughter felt displaced. She loved them and wanted to hold them and play with them but she was no longer the center of my world. I have noticed that whenever I babysit for a friend, she suddenly wants to read me a book or hug on me.
I am a SAHM, but I was a teacher before I had my children. I did not plan on ever putting my children in preschool, but I did put my 6 year-old in preschool when she was four. I needed a break and so did she. I noticed that you run a preschool and child care. This could be adding to her wanting your attention. She may not want to play with the other children because she sees them as her competion for your love and attention. She may want to hug and kiss you because she is reassuring herself that you love her the most.
There are a couple of things that have really helped me. First, I talked to her about it. We decided together that when she wants to hug and kiss me that we do it four times (she wanted 10, I wanted 2, we compromised on 4). I go to her level, we squeeze four times and kiss four times and then we're done and she has to go play. I also reassure her that I love her by telling her often.
Putting her in preschool really helped her make new friends and feel more secure when I am not around. We also scheduled more time with Dad. I really feel that it helps a girls security to have time with her dad, so I would send them to the store for something. Sometimes he spends time with her in the evening doing a puzzle or something.
I also found a really great babysitter. She is a high school girl and my children LOVE her(my husband teaches at the HS, but you can get good references from other moms). When she comes she makes my children feel special. She can bring a game that we don't own, or do crafts. My 6 year-old asks when she's coming over to "play".
My daugter is still clingy, but it has become so much better as I have tried these strategies. I would like to say that I came up with them, but these are ideas that were shared with me when I was close to losing it. I hope that these ideas help you. I know it can be so frustrating. Good luck!