My first question would be how old are your kids and did they all start wanting this at the same time? If it occurred at different times, then you might want to take a step back and look at yourself. When this happens it is usually a sign that the kids feel ignored and like you are not considering them or their feelings. However, if you children and are close and all decided this at the same time, then I think it is time to line them up and sit down with them and have a talk. Ask them why they want to leave you so badly when they know how very much you love them? Ask them how they would feel if you wanted to run away from them (but explain that you dont after they answer.) While they may be obstinate and not helpful at first, the longer you talk to them the more they are likely to tell you. One thing that is the hardest for us parents is not to get frustrated and angry and either bicker with them or stomp off for a while. You need try to open up the lines of communication and look at how to bring your family together. They are kids. You are the adult. This is the time to show them the difference. Teach them the appropriate way to deal with feelings they are having, which is not running away. I think by leaving them all alone together, you could possibly show them that they take you for granted, but you would also be teaching them numerous other negative things as well. Like, that running away IS acceptable or that if they are bad enough you will just leave them. That's not what you want. Instead, try to make a little extra time to spend with them together. Organize some family outings. Also, try and set aside one on one time with each of them every week. They need to feel like their world is safe, secure, fair, balanced, and understanding.
I would like to point out that I am NOT some all nurturing, don't punish your kids type of mom. I am just saying that in this particular situation, that's probably the best route. If they are ganging up on you, though, then I would separate them. Talk to them as a group AND individually about the problem. If it is just them missing their father or acting on curiosity and a stage, then there are steps you can take to deal with it. If it is actually something in the home life that is spurring this, then that needs to be addressed. If your family is experiencing any financial troubles, then this is a common reaction in children, and there are ways to work through it as well. Feel free to message me here. Or look at other responses I have given to other mothers.
In regards to the Pinocchio thing, if you have older children around, I doubt that would last long.
I wish you all the luck in the world!