How do dentists handle children refusing to open their mouths during treatment?

You should prepare them even before coming to the dentist. Depending on the age of the child, talking to your child about what is going to happen at the dentist and assuring them is a good strategy. Always use positive words. I find other things that help are reading books or watching cartoons such as Peppa pig, where there is an episode on going to the dentist. When they see someone else doing it, especially someone their age, it might help them manage their expectation as well.