Can Your Neighbor Force You to Cut Your Tree

My question involves personal property located in the State of: California

Can my neighbor force us to cut down our tree or take legal action against us? Our tree which was there before we moved in has roots that have started to grow on our neighbors property. The roots have caused some damage to the driveway, or this is what our neighbor has suggested. The neighbor called the city so they could begin digging up her driveway. After she dug it up she let my husband know that our roots were the cause of the damaged and informed us that we need to cut down are tree. We did get a couple of estimates to see what the cost would be to cut the tree down but all were really expensive. We told the neighbor we would look into cutting the tree down, but this was really expensive and we would have to wait until we had the funds to have it cut. But my neighbor decided to allow her tenants to work on the driveway by burning and cutting away at the roots. They also cut away at the branches that were hanging over but I have heard this is okay. Now she sent us a letter stating (via certified mail) she will take legal action in two weeks if we do not cut down the tree. What are our rights?

Can Your Neighbor Force You to Cut Your Tree