Problem: You've been staying at home with your little ones and they're rather attached to you, to put it mildly. But sometimes you have to do things like go to the doctor, or to the gym, or they get old enough where preschool would do them some good. You need them to stop clinging to your ankles and screaming like you're running them over with a bulldozer.
Solution: There is none. If you're here, it's already too late. Okay, not really, but parents of babies, take note: Leave your children on a regular basis. I'm serious. It seems fine at the time, you think they'll understand later when you have to leave them for a bit, but if you don't get them accustomed to it when they're smaller, it's hell. It could be hell anyway, depending on your kid. It's hardly ever easy, especially if they're used to seeing you all the time.
But for us, for my family, it's on the pathetic side. Here I have two three and a half year old who absolutely throw holy hell when I attempt to leave or do anything without them. They have never even been alone with their father since we moved to Florida two years ago. And now, they won't accept it.
If you're in my position, you have to take a firm stance. Understand that they don't know what they are talking about. You're not really breaking their hearts. They're not really that scared. They're just doing that thing they do where little things become wicked important just because. Think of yourself as the pink socks. They couldn't care less, really, whether or not they're wearing the pink socks in the big scheme of things, but at the time, they will roll around in a puddle for thirty minutes because you put them in the blue. Same thing. Just do it. Just go. It's going to suck. But it's never going to suck any less. The longer you put it off, the worse it gets.