Thank you for using JustAnswer. I am Loren, a licensed attorney, and I will do whatever I can to answer your question.
This is a common legal question, and the answer is that the tree owner is liable under trespass and private nuisance
theories. Among the remedies are cutting the roots at the property line; there is a caveat that this must be done in a "non-negligent manner," which the courts did not further define, but probably would include avoiding killing the trees or causing them to be in danger of toppling in a high wind. Also, you can not trespass on your neighbor's property to do the trimming.
The best practical advice is to hire both a contractor
to give you a dollar estimate for the damage done to date, and a licensed arborist to give you a written opinion that the trees caused the damage along with professional advice on what can be done "non-negligently" to prevent future damage.
Show all this to the neighbor, and ask for cooperation again, mentioning that you will have to sue if he/she does not correct the situation voluntarily.
I hope this is helpful. If you have more follow up questions please let me know. It is never a problem.