Size and/or gender of the officer doesnt matter much on something like a traffic stop in town like that. If they were out in the middle of nowhere, maybe. Intimidation does factor in when there's no one else around to see what happens. Also, as Tarmac said, there could be alot of reasons why she had trouble with the holster. In competitions you learn real quick how important it is to be comfortable with the rig you use. Cops dont have much in the way of options, but it makes it all the more important that they become familiar with every inch of that belt and train their muscle memory. She was probably new, given your description, but I try not to assume either way. No matter how routine this might have been, adrenaline almost always kicks in when you are confronting someone, no matter how minor the infraction. Different people react to the adrenaline rush in different ways.
As for her approach to the car, and the surrounding area? Well, all that stuff has to be processed fairly quickly, when other things are on your mind. Without any actual fear that he might be dangerous, she did the right thing by keeping him in the car where his mobility is limited, and made the best of the situation. She may never have noticed the school, and it may never have crossed her mind that a miss or ricochet could go that way. It often doesnt occur to people who arent comfortable with guns or are inexperienced. Some police officers are in these categories, right or wrong. She had to focus on the situation in front of her, and make firm decisions one way or the other. Showing distraction or indecision is a good way to turn an otherwise calm situation scary. Either way, she did what she had to do and the guy left. No matter if she was scared, new, freaked out, or high as a kite, and even if things werent ideal, I'd say it was handled as well as could be expected (of course I wasnt there, I didnt see it, and I know nothing of the situation except what you described). The only way to know just how much of the scene had processed in her brain was to have it go bad and see how she reacted. Thankfully, that didnt happen.