Hi, L.. Well, you're on the right track! Yes, take her out of the stroller as long as she holds your hand, and yes, take away that freedom when she decides to disobey you. Absolutely. Unfortunately, she's at that age when her attention span is limited, and she doesn't yet have the patience or the appreciation of limits to keep within your rules. There's nothing in it for her, you see, to obey you. She doesn't understand that she could get hurt if she doesn't walk close to you. And she shouldn't have to walk around worrying about that -- that's what parents are for. So understand that from her point of view, you adults are being totally unreasonable ( :
Unfortunately, you may have to put up with some screaming for the time being. She has begun what we call the "terrible twos." She wants her freedom, she wants her power, she wants her curiosity satisfied, and she wants her sense of accomplishment, so she will have to come up against the fact that she is not the center of the universe, and she can't have everything her own way. This is very frustrating for a toddler! But this is a milestone in her development, and the only way out of it is THROUGH it. It's very important that she has a sense of power and ability, just as much as it's important that she be safe in public places. Finding the balance is not easy.
Try telling her every 30 seconds or so (to keep her focused, because she has no attention span) what a GOOD, BIG GIRL SHE IS for holding your hand. Praise her, smile at her, give her a whole lot of attention for holding your hands. Make it a lot more pleasant to walk holding your hand than to run off by herself. Point out interesting stuff to her. Tell her what you are looking at in the store, and what you're going to buy, and what you're going to cook with it, etc. Keep her interested and feeling involved. I think she's craving that attention.
You see, she knows that if she runs off, she'll get more attention than by just walking calmly beside you -- negative attention, but attention just the same. Talk to her, interact with her, make it interesting to walk holding your hand, then she'll want to do it more. Give her that reward for doing things your way. Make it very, very pleasant and fulfilling to follow your hand-holding rule (candy is NOT necessary, just attention).
If that doesn't work for some reason, the only other alternative is to put her on a toddler leash, but that won't keep her from screaming when she comes to the end of the leash and screams because she's still restrained. I would use a toddler leash (I think they call them tethers) only as a last resort. She sounds like a very, very smart little girl, and I think she may respond to the extra attention.
I hope everything works out very well for your family, and that you all get through the terrible twos with a minimum of toddler drama.
Peace,
Syl