Mother Guilt

Today I got so frustrated with my kids and now I feel.... you guessed it, GUILTY. I took them out all morning and well into the afternoon on errands. They were tired and wanted to go home after about an hour and a half. When that happens they start whining, and arguing with each other. It just grates on my nerves. By the time we got home 6 hours or so after we left, I was ready for some alone time. My 3 year old daughter kept coming to sit with me and wanted attention. I kept telling her I wanted to be alone. She was showing me a coin and asking me about it. I threw it across the room so she would get off my lap and out of my space. It hurt her feelings and she cried. I know, bad mommy.
She is so clingy lately. I know that I have been away from her a lot between work and the internship. Her clinginess is justified (that alone makes me cringe with guilt). Children do whatever they can to stay close to their parents, even if it becomes dysfunctional. I don't know how to meet her need to be close to me all the time without getting irritated. Sometimes I don't feel like talking to her or anybody else. I need quiet time. Maybe I just want it, maybe its not a true need. I don't know. I worry that I am creating issues for my daughter by making her feel rejected. My heart wants to break at the thought that my baby might feel rejected by me. I love her so much and want to give her a safe and secure mother-daughter relationship. I am feeling like a horrible parent right now. I hope that somehow God can see my true intentions and feelings as a parent, and fill in the gaps for my kids where I am falling short.