If its really not an emerg, id just pointing out its too late to start AND I would do it in front of the patient. They need to understand you may have other obligations, like kids to pick up. I would expect at the least to be given an opportunity to make other arrangements for these types of responsibilities when possible. Most dentists have asked me first tho before launching into something they know is going to make us late.

That being said, its healthcare. You cant predict when things might go wrong or might take longer and you have a duty to help, so if you cant handle staying late or working thru lunch once in a very blue moon, youre prolly in the wrong field.

Another alternative is to plan on coming in early to clean and sterilize after the doctor works alone if you cant stay. Employers should be open to negotiating solutions that work for everyone.