My 4 yr old won't behave in public or with other children?

I really need some good advise, I have a 4 yr old and she is such a sweetheart, shes smart and with adults shes very charming, but she is an only child and she does not interact with other kids very well. She also will never listen to me when I take her out in public, I really feel like i have no life anymore because no one wants to hang out with me and my daughter because of her bad behavior. My cousin was hanging with me and my daughter today and she made an accuse to leave early because of my daughters out bursts. We went to the mall and i was so embarrassed because my kid was running around knocking things over and screaming No to me! I almost had to pay for something she broke on purpose. My cousin has a 2 yr old and my daughter is just horrible with him. ZShe's a sweetheart when we are at home and for the most part listens but all my rules are out the window once we leave the house. I couldn't leave the mall cuz' my cousin drove so i was and still am at my wits end. i have a throbbing headache and always do after a day out with her. We r suppose to go swimming Wednesday but i don't have a handle on her anymore and i don't want to be cooped up in the house or avoided because of my daughter, i don't know what to do anymore. any help would be grate. Also i have tried spanking and time out and revoking things thanks