Terribly sorry buddy, did not see this until just now, really sucks!!!!!!
BUT, kids are far more important, as you are as well so the car died to take care of you, be glad it was just the car.
Do get your neck and back checked out as injuries sometimes take awhile to kick in, enough force to break a seat is enough to injure you and your kids.
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Unless the frame rails are bent at or past the suspension/subframe mounts a good shop can make the car drive just fine, if bent there I would never accept it being repaired.
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Since she was pushed by somebody else then the hit and run driver is the one liable but likely not even insured if in an older vehicle especially or drinking if in a newer one......likely your insurance will have to foot the bill on this one but it should not raise your rates, if it does look for a better company.
I have used State Farm for around 35 years now, they are incredible to deal with, always so.
Most sincerely
Rick