If you read the book, "Parenting with Love and Logic", it talks about the natural consequences of the poor choices children will make when left to their own devices, but you have to be willing to allow those natural consequences to happen. If they won't come to the table to eat when it is time to eat, they don't eat. Period. They won't starve to death. You make it clear to them that this is their time to eat and it is their choice not to eat, and they are not going to get another chance later. So later, when they are hungry, instead of saying, "Well, you should have eaten when it was dinnertime!", you empathize, saying, "I'd be hungry too if I didn't eat dinner." Same thing goes for bedtime (though it may be more applicable for the 6 year old than the 3 year old) - they don't have to go to bed or go to sleep, but you can tell them they have to stay in their rooms. They can stay up playing or reading or whatever, but they need to stay in their rooms. Then the next day, when 6 year old is having to go to school and all grumpy from lack of sleep, you just say, "Yeah, I get really grumpy when I don't get enough sleep either. Have fun at school today!" Let them experience the consequences of their decisions, rather than imposing any consequences on them yourself - that way, they start to accept responsibility for their choices, rather than casting you as the bad guy and blaming you for why they are unhappy.
Along with "Parenting with Love and Logic.", I also recommend "How to Talk So Your Kids Will Listen and How to Listen So Your Kids Will Talk". It's great for learning how to communicate better and getting your kids on the same page.