You need to teach her boundaries.
All kids go through phases of being real attached to Mommy.
But at the same time, you need to teach them boundaries/how to be self-reliant/how to entertain themselves etc. And it is not being selfish on your part... it is HELPING your daughter, become, more evolved. And in her sense of self.
Telling your child "Mommy needs some time to myself" is not being mean.
Or telling her "Mommy is busy now, I have to clean the bathroom..." is fine.
Or "Mommy can't play with you now, I have grown up things to do."
Its OKAY to say this.
It is life, it is just how it is sometimes.
You will not traumatize her by telling her things.
I tell my kids things like that too.
Ever since they were Toddlers.
And they don't get hurt feelings or tantrum about it.
They, understand, AND they have come to know the daily running of the house and of Mommy's routines and of their routines. TOO.
It is life.
Does she have, friends?
Or is she involved in any extracurricular activities or have any hobbies?
If not, then nurture that in her.
After a certain age, it is not "cute", when an older child is so demanding and clingy, of their Mom or any primary caretaker.
Both my kids really are attached to me and call me cute things in affection. BUT at the same time, they are also very independent and self-reliant and are perfectly fine doing things on their own when I am busy.
Try asking your daughter, why she is so clingy with you?
I've asked my son that. He was more clingy with me than my daughter, although they are both very close to me. And he told me simply "because you are so cuddly Mommy, and so cozy.... and it makes me feel good." Okay, fine, I told him. Mommy loves you to, but we both have things to do... and you need to let me. And he was fine. Because we talked about it. I told him Mommy is always here if you need me. You know how to talk. Then I would go and do whatever chore I had to do in the house.
You SHOULD be able to socialize with other adults, without her being at your hip and demanding your attention.
Speak to her.
Tell her it is not real nice of her, to interrupt.
I have told my kids that.
It is just being honest and teaching them concepts etc.
Manners.
Boundaries
and social cues