Normal for kids "sticking" to me..always ?

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I want to be a good mom to my kids. I am still learning how to be. I think most mothers like can get upset with our kids' behaviours. Do you think so ? Take me for a real example. : My kids often follow me around. To the kitchen, they follow. To the room, they follow. To the bathroom,they also follow! Is it normal ? Sometimes, I would tell them to play outside as mommy wants to do some work. But still they will follow behind. Any idea how to prevent them from following me ? And oh, my 1-year old daughter tends to push me away when I am standing. If I don't budge, she would cry. But if I do, she would stand in front of me and start crying ! What did I do ??