As someone who works in an ER, the resident's behavior was unacceptable. That being said, it is almost standard practice to place young children in a papoose while suturing them, especially for a facial laceration. Even if they stop crying prior to the procedure, there is a high likelihood they will start again once the procedure starts. You also don't want any sudden movements, especially them grabbing your instruments, while working on their face.

As for making the parents leave, it depends on the parents. Despite their intentions, parents rarely help calm the situation. If you can sit quietly and hold their hand - great. If you are hovering over their face, the area I am trying to work on, repeatedly telling them not to cry and everything's OK, that usually just makes things worse. Kids that young generally cannot rationalize the situation, and just about any stimuli from the parents generally makes things worse. It's like when a kid falls on the floor. If you ignore it and don't make it seem like any big deal, most times they just get up and act like nothing happened. If you start fussing over them, even if to reassure them, they get the idea that something should be wrong, and freak out about it. Same thing happens with medical procedures.

What I get from your story, it that a resident definitely behaved unprofessionally. Based on your description of him of being young, I am guessing you didn't have much confidence in him from the moment he walked in the door, and then proceeded to tell him how he should practice medicine. I am in no way agreeing with his behavior, but nothing in your story proves your daughter would have had any worse outcome of you just let the resident do their thing.