What's the best way to find a doctor who likes Obamacare plans because mine doesn't?

Your doctor either accepts your insurance or he doesn’t. You choose a doctor when you sign up for the insurance every year. There’s no reason for your doctor to know how you purchased the insurance unless you tell him.

There's no such thing as an "Obamacare plan". Obamacare isn't insurance, and it doesn't have any insurance policies. All it does is make existing policies less expensive and more accessible.