Just want to say I'm right there with you. My daughter is about to turn two and, like yours, she'll play if I'm sitting right next to her, but heaven forbid I get up to start a load of laundry!
They can have such interesting and unique personalities, huh?
That leaning tower that the other ladies gave you is a good idea. I'll have to try that as well. Is that just one of those step stools that lean??
Could you maybe put your child in their crib for some alone time when you need to get things done? Mine seems to have the same personality as yours and she enjoys her "alone time"..Good luck!