My older brother went through a stage of being obsessed with Snickers. By the way, this was so long ago I think they were called Marathon but that's by the by. Anyway he would save a bit of his lunch money and wolf down at least two bars on the walk home from school. Inevitably he wouldn't be able to eat the nutritious dinner prepared by my mother (and occasionally not so nutritious - Findus Crispy Pancakes anyone?) which would leave mum, who was working and raising children and trying to maintain a healthy soap habit, annoyed to say the least.
As anyone who's been cheated on by a guy knows - they never hide the evidence; so when my mother found all the snickers wrappers stashed in my bro's school trouser pockets, she realised her corned beef hash had been usurped by nougat and marketing. My mother is a canny lass and she has always believed that revenge is best served cold and the next evening it was. Instead of meat and two veg she served my brother three snickers bars fresh from the fridge. He thought he had won the lottery! The next evening she did the same and he ate his peanut and caramel based meal with a little less gusto; by the third evening he was begging for spaghetti bolognaise. To my knowledge he has not eaten a Snickers since.
You know where this is going right? If you're concerned about how often your kids choose to be parked in front of a screen, pick a period of time you're comfortable with (I'm thinking at least a weekend) and declare it a screen feast. Tell your children you trust them to self regulate and you never know you might find they can. Our greatest fears are usually only terribly poor predictions, who knows with unfettered access sitting in a virtual world might not be as desirable? Perhaps not, maybe they'll play Minecraft for 48 hours but the beauty of that is when you next impose a cap you can say, 'Darling, when I let you choose you forgot to eat, so I think I'm gonna need to help you with this.' Kids have an inbuilt fairness barometer, nothing sets that thing off more than being told to do something just because adult says so. Being able to give them a tangible reason for denying them what they want can make things a lot easier.
Finally make sure your own house is in order. Are you asking your kids to do something, you can't do yourself - do you send them off to bed and then settle down for three hours of mindless telly? Are you providing healthy, fun alternatives to screen time? Are you trying to sell homework over Super Mario Kart, coz even I'd rebel with that choice!
If you find a screen feast does nothing to alleviate your tension remember that you're a parent, not a psychic - who knows how your children's passions may shape their future. Perhaps your little addict, is a budding TV producer and what if your boundaries stop them from achieving their dreams and making the millions that will keep your heating on when the government has run the county into the ground? Okay this is very unlikely but the thought might stop you from tearing your hair out.