You need to file a claim on (your) auto insurance ASAP.
Your auto insurance will pay for the replacement of the tree. IF the tree is dead, since bent over, then they would pay to remove it, and pay for a new tree in its place. But, if the tree is not dead, but only branches came off, then you (might) not owe them (nothing).
Either way, if you are sued, then your auto policy will pay for a lawyer for FREE to defend you.
And (no) can't counter sue the parents for the damages to your car. The reason is, that to avoid hitting the child, you hit the tree instead. I know it makes no sense, since in many accidents, like an example that you avoid hitting another car, but hit a tree, guard rail or curb etc, that since there was (no) contact, then can't sue the other person for avoiding an accident.
Let your insurance make the call, to pay or deny.
retired auto adjuster