First and foremost, I most definitely would NOT be comfortable if I knew my 3 year old was outside unsupervised with another child - especially in the world we live in today! That in itself is asking for trouble.
That aside, when your kids are with a daycare provider (private or public), it is the responsibility of that provider to ensure the kids are safe and supervised at all times. Given that the damage occurred when they were unsupervised on her premises, she should be somewhat (if not fully) liable for the damages. This damage is NOT due to your negligence so I don't think it should be your responsibility.
If this individual has auto insurance, I would think a claim could be submitted to the insurance company for coverage. If so, there would probably be a deductible - perhaps you could assist with that. Most deductibles are less than $700...but the cost definitely should not be yours to bare alone.
It is a tough situation b/c of the relationship you have with the "provider" but honestly, I don't think this should be your responsibility.