Unfortunately, I would not bet on the insurance co. willing to replace the tree. Replacing a grown tree is a big undertaking and there's no guarantee it'll take anyway. Insurance company would be trying to pay only for the immediate damage (as in "damaged bark") and it would be peanuts compared to the actual costs of replacement involved. On the other hand, you way be able to convince them to pay for cutting it down.
There was a very interesting and relevant thread here (long time ago), let me see if I can find it ...
Here, found it: http://www.homeownershub.com/garden/tree-damaged-by-car-accident-insurance-problems-25211-.htm , see if you can glean some useful details from it.