My toddler always wants to be where I am, but I can't play all day. How do I get her to play by herself so I can get things done?
Rather than trying to get your child to leave you alone, do as much as you can in the same space with her - bring your tasks where she is and invite her where you are. Some things that are fun for three year olds in adult spaces include:
*giving her a wash-tub of water and unbreakable things while you're doing dishes
*make up a collection of "cleaning products" just for her - rags for wiping, a kid-size broom, some spray bottles with kid-safe contents like plain water, soapy water, white vinegar. Label the bottles so she can play with reading, too.
*get her some "ingredients" to play with while you're cooking - flour, rice, beans, water, oil, vinegar, as well as inexpensive spices and food coloring. She might want to help cook for real, but lots of kids love to just mix things up like mad scientists.
*have a sturdy stepstool so that she can get up and see what's going on over her head.
*explore textures together - if you're folding laundry, how do different fabrics feel? how do they hang when you hold them up or wave them like a flag? If you're outside, how does grass feel? Leaves? dusty dirt versus gravel?
*if you're settling the baby, think of "quiet" games to play together - whispering can be fun for little kids, and blowing bubbles, or a game where one person pats your hand in a gentle pattern and the other imitates it.