The person who hit the golf ball would be liable, since he or she was the one who did the damage. And the golf course would also be liable, since it was one of its invitees, doing the activity that the golf course invited them to do, that did the damage. The homeowner would have the option of pressing a claim against either, though since the golf course is larger, presumably has insurance, and is easily identified, they'd be the logical choice.
The Answer(s) provided above are for general information only. The attorney providing the answer was not serving as the attorney for the person submitting the question or in any attorney-client relationship with such person. Laws may vary from state to state, and sometimes change. Tiny variations in the facts, or a fact not set forth in a question, often can change a legal outcome or an attorney's conclusion. Although AttorneyPages.com has verified the attorney was admitted to practice law in at least one jurisdiction, he or she may not be authorized to practice law in the jurisdiction referred to in the question, nor is he or she necessarily experienced in the area of the law involved. Unlike the information in the Answer(s) above, upon which you should NOT rely, for personal advice you can rely upon we suggest you go to AttorneyPages.com
and retain an attorney to represent you.