I also had a tree land on my house during the hurricane, luckily it didn't do too much damage, just needed minor repairs. Just finished cutting the tree up, have to finish the rest of the clean up. The soggy ground doesn't help. Trying to look on the bright side, my neighbor who helped with the tree removal gets a big load of firewood.
The most important thing to realize, is that you and yours are safe. Hoping everything works out for you in your dealings with the insurance company. Prayers to you and your family.