Re: Toddler running from you?
When DS went through this, I just stopped taking him places. I know it isn't possible for everyone, but we just worked it out so that he just never left the house. When he really started bugging us about leaving the house, we'd explain we can't trust him not to run off. So he'd tell us he wouldn't do that. When he did it again in public, again, another loooong amount of time basically quarantined to the house. (Dead of winter so no parks either!) It honestly worked!
We also have a rule that must ride in the cart or hold onto the cart or someone's hand at ALL times. When he was old enough he did want to walk, it was a lot of repetition. Don't want to hang onto cart or hold hands? you go back in the cart(promptly followed with whining/crying/tantrum - ugh!) He's 3 now, and its much easier to go out in public with him.