J.R.
I have been a pre-school teacher for 20+ years, and now work as an assistant director at a school, so I'd like to think I speak from some experience. There are a number of factors here which is why your question is so long... (and the answer too). Part of the reason for taking children to pre-school is so they can begin to learn some socialization skills, which includes conflict resolution (yes even 2's begin to create coping skills for this in their own way). Your daughter is (for now) the only child in the home, so she has never been exposed to sharing, cooperation and similar concepts. She is accustomed at home to having what ever she wants as there is no competition. When a sibling comes along some of that will take care of itself. It may be the child pushing is not a first-born and is picking up aggressive tactics from older siblings. There are agressive people in the world, so learning to deal with them is important (which begs the question does that need to start at age 2???? apparently so) Another noteworthy point is that it is not uncommon for 2's to regress a with potty training when they start school for the first time. All that being said... I, as a parent and teacher see several red flags... 1. The accidents are increasing not decreasing over time. 2. She has picked up the behavior and is using it as a tactic in new situations. 3. Scratches on the face that are unexplained. 4. If this is a class for 2 year olds there should be multiples of the same toys because while we begin to teach about sharing they really don't have that skill yet, so you reduce competition by having multiples.
I do not think she is too young to be in a program. But it sounds like this particular program may not be a good fit for her. I don't like to make judgments about any school. The teachers may be working very hard to help re-train all the children from this behavior, and the pushing child may have some particular issues, which legally the teacher cannot discuss with other parents. But if that is the case they need to have an aide close to that child at all times. It might be worth looking for another program for your daughter. You do not want that behavior to become dominant and have her use it on a new sibling. In the meantime talk to the teachers more, see what you can do together to work on the issue. Teachers often feel on the defensive, and not being able to discuss particulars makes that more the case. But the "what can I do, as a parent, to help" approach may get you farther. Ask how they explain and redirect your child so you can duplicate that in other settings. It is not out of line to speak to the director. She should be aware of any dynamic in the classroom and be helping the teachers create strategy to benefit all the students. This is your opportunity to teach your daughter that some people do push... It is not nice. She should go away from people who push. Tell the teacher when it happens... (give her the coping skills)
Try to set up play dates with other students in the class on days when there is not school so she can build some friendships. (Ask the teacher who she does get along with) The more the teacher feels she is your advocate rather than adversary the better.) There is so much here.... hang in there, they don't call it the terrible 2's for nothing. These are children who finally understand they are a separate entity from their parent and they are exploring what it means to be an individual. They have not yet figured out that others are individuals too. Good luck. Feel free to write back and let me know how it is going (____@____.com)