BSD, Now that you have answered everyone’s questions here is what I know from working in the insurance industry for 9 years. Knowing that the older brother chases and hits your daughter, YOU were negligent allowing your child to play there. Furthermore, the boy was NOT chasing her at the time, she was hiding from him. No one pushed her, she got hurt on her own. To answer your question about your own insurance paying for your daughter getting hurt in someone else’s house. Yes they should cover it. If you fall outside, the insurance company doesn’t ask you why you aren’t suing the city or the homeowner in front of who’s house you fell.
As far as car accidents are concerned. The two parties driving the two vehicles wind up in a law suit if there are long term physical damage or if one does not have collision insurance and wants the other to pay to fix the car. The passenger in your car would not necessarily sue you if you had a car accident and bumped into the car ahead of you, or if you crashed into a tree or pole. How would you feel if your friend sued you?
And as I said earlier, you have 18 months to put in a claim. You should see some healing progress within at least 6 months. At which time you can determine what you should do. I highly doubt if you went to an attorney today they would take your case seriously. And obviously you should check with your insurance company or rather get a referral from your pediatrician to a plastic surgeon and see if you get approval from the insurance company before you think “law suit”. Speak to the plastic surgeon first before you blow this out of proportion and put both children through the ringer. And I would suggest to you, that if anyone hits your children in the future, you do NOT allow your children to play in their homes. That would be the best way to protect your children from uncontrollable bullies.