planning and this work often involves someone picking one of their children to be a trustee after they are dead. People often ask if two children can do this together or how they should pick. I basically say to them, “you know your children.” The implication is clear. You know which child you can trust and which you can’t. Every parent is the same.
You know your daughter. You stated that she is extremely sensitive. This knowledge needs to shape your response to the situation. I can empathize with you. I have a three year old. Whether she bumped her head or lost an arm, the reaction is the same. I know that. It shapes my reaction. When I see something minor happen and the reaction comes, I tell her to stop crying. Nicely, but I say that she is okay and needs to stop. She almost always does and is totally fine and happy again.
It is unusual for a child to be pushed twice and have it bother her so much that she bursts into tears hours later. It seems like this might have more to do with her sensitivity than what actually happened. I would make the teacher aware of what happened and ask her to keep an eye out. That is an appropriate response at this point. Escalating things when the conduct doesn’t necessitate it just makes the authorities take you less seriously. I get that this is hard, but your conduct so far with the school and in this thread show that you might be a bit too close to the situation. Give it time. Cool off.