Don't worry. A stye that can be called hordeolum is a common phenomenon among most of us. They will not cause big problems for and they often get better without any treatment. After it bursts and has released pus, they will go away on its own. Most styes will disappear within three weeks. But you must remember not to burst the stye by yourself.
You can apply warm compress to relieve eye styes for your children. Put a piece of clean cloth or flannel in hot water. And then wring them until they don't drop water. Then apply the warm cloth or flannel on your children' eyes. Remember that you can't use very hot water, because children' skin is more tender.