You've got both a personal & media problem at the moment, but, you probably should not quit golf, in fact, it is probably a good idea to get back into the game as soon as possible. Since your infidelity issue is probably not directly related to your work/golf, there is no good reason to let your work & the game suffer because of the other problem.
About the whole cheating on your wife thing: serious problem, but ultimately a matter to be resolved between you & your wife & kids. And beyond that, to be resolved by/within yourself, since ultimately you are the only one who can make radical changes to your behavior (and as shown by your mastery of a very difficult sport, I am sure you are more than capable of getting unwanted habits under control - after much work).
In fact, instead of giving up golf or taking a long break from it, you might want to take a break from sex, re-evaluate your relationship with it, and perhaps find healthier alternatives to cheating if you decide to go ahead with being a married man (of course in this current marriage that may not be entirely up to you). The other alternative is to become single, have as many girlfriends as you want (and of course honor your commitments & obligations to your current - perhaps soon to be X wife & the children).
Back to this whole issue of golf & sex/infidelity. The two do not have much in common. You've got a problem managing your private life, but you are an excellent golfer - so, while you work on repairing the damage in your private life, it may be helpful to continue with what you are very good at - golf.
That's just my take on it. Good luck with everything, don't beat yourself up too much about past mistakes - as humans everyone is vulnerable - as long as you fully own/accept your past mistakes & attempt to live better in the future, I am sure you & others will be able to forgive you.
I think that's about it Tiger. Get back to golfing, simplify your personal life/work on any past/recent mistakes, apologize & make amends to everyone that you feel is owed that, and take good care of yourself & your family - don't worry, do those things & things should work out well for you. You'll be back on top of your game & living a simple & happy life soon, if you do the required work.