Welcome to the area. You probably need to do some reading on the health care system
The kids will get a paediatrician rather than a family generalist. You can usually choose any paed you like for the kids .. For the adult generalist you may have to choose one from an approved list - depending on your health care plan.
I'm a bit further along the lake so i don't know any in your area I'm afraid.
There's a Facebook group called "FOR SALE, FREE or WANTED in Vaud/Geneva" and similar question has been asked there a couple of times..Or you can just ask it again if you get no results here.