I really like Karma's suggestion to follow her without letting her know you're there. I've infrequently done that with my grandchildren. The difficulty in doing that is that my granddaughter is fearless. Even at that age she would find a clerk to help her find me. At 8 she still likes to hide from me. My daughter also liked to hide at that age. Perhaps physically leaving Mom is a part of learning to seperate?
For the hiding, I stay in the same department. She gets bored when I don't look for her and comes out of hiding. I was too anxious to do that until she started school.
I also agree that if you didn't give her a consequence within 10-15 minutes it's too late now. I disagree with putting her in her room for 1-3 hours. This has no meaning to a child this age and is pure punishment at any age. Our goal as parents is to teach using methods that actually show our children how their actions have consequences. Putting them in their room most likely will make her and older children angry which then adds to your problem.
I try to use Love and Logic. Their ideas make sense to me. For those who aren't familiar with it a very shortened explanation related to this question is that the consequence relates to what you want them to learn. And you deliver the consequence in a loving way.
Sometimes I cannot think of a logical consequence. When they're disruptive for any reason and don't stop when politely asked to stop I do send my grandchildren to their room. They can come out when they can be good company. I didn't think of that until I saw my daughter use it.
When I can't think of a consequence such as in your situation I then find a way for everyone to be safe. In this case I suggest that you find a way to keep her in the room with you. Use a room with a door and shut the door so you'll hear her leave. Or get her busy doing something in a room with a door and again shut the door. You might even put a small bell on the door. Tape the little bell to the upper frame so that when the door is opened it rings. It is a bit of a hassle since you have to move the bell back inside each time you enter.
When my granddaughter was that age she left the daycare facility while her mother was talking with an employee. The day care was just a few blocks from my house and she thought she could walk to my house. She walked the opposite way. The employee walked one way and my daughter walked the other way and fortunately they found her within a few blocks of the center. She got part of the "stranger danger" lesson then.
Not everyone is kind. There are people who want to hurt you. There are also people who really like little girls like you and they might pick you up and take you home with them. I'd miss you so much. I don't want you to be kidnapped. After this discussion that started with Mama telling her how scared she was, Mama reinforced the idea that Monet had to always be with Mama, Grandma, teacher etc. by answering questions which Monet asked. The telling her she must always be with one of us was repeated and repeated.
Monet, as far as I know and remember, has never ran away from an adult while they were outside. Every once in awhile she would tell me she didn't want to be kidnapped as she stayed close to me. This didn't hold up in Fred Meyer where she and I shopped frequently. She felt safe there and no amount of telling her that she could be kidnapped in a store convinced her. I tell you this because walking out of the apartment and down the street is just the beginning.
I started putting a blanket on the bottom of the shopping cart and giving her something to do worked until she got too big. If I didn't do that I had her help me push the cart by putting her between the cart and me.
Running away and/her hiding is such a fun game for her she still tries to hook me from time to time but rarely now. I found that I could take the fun out of the game if I didn't respond at all. I'd follow her or look in the rounders. When she saw me and would come out of hiding or see me and come back to me, I wouldn't say anything. Once she realized I wasn't playing she'd stop.
I think that your daughter most likely left because she was exploring. At that age some kids have no fear. Perhaps you could walk the neighborhood with her telling her that it's only OK to walk around outside when she's with an adult. She can explore with you.
At first I questioned the wiseness of putting fear in Monet's mind. She talked about not wanting to be kidnapped for quite awhile and I wondered if that was too heavy a concept. After some time of thinking about it I decided that kids do need to know that some things are not safe. Saying something is not safe is not enough enformation for my very energetic and inquisitive granddaughter. Even at 3 she wanted to know why it wasn't safe.
I think that in many safety issues just letting the child know that you will not let her go out on her own and using some safety measures is a consequence. She has lost your trust in that situation. Perhaps that's why it's a consequence.
As a preschooler, my granddaughter left their apartment and made it to the lobby at which time an employee called me. It seemed that having a stranger stop her and give her a bit of a lecture was enough. I don't think she left again. I did make sure the dead bolt was always locked and much to my surprise she couldn't figure out why the door wouldn't open.
I have two devices to put on lever style doors that I would be glad to mail to you if you have that style of "knob." They're in unopened packages; brand Safety First, I think.