I am a father of 2 boys (5 & 2). I will often take my 5 year old out with me for a quick nine, usually later in the afternoon when it isn’t as busy since he has a tendency to use his playground voice and I don’t want to disturb anyone.
My main goal is just trying to make it a fun for him - he hasn’t shown an interest in playing yet (aside from putting on an occasional green), but loves riding in the cart. He also likes looking for balls (the chewed up ones from the lawnmowers are his favorite to find) and unbroken tees. He has asked about what a divot tool is, so I explained to him what it is for and how to use it, and now he’s excited when he gets to fix a ball mark. Same thing with filling divots with sand mix,and raking bunkers (which he is surprisingly good at). Maybe he’ll be a greenskeeper someday, who knows?
Regardless of whether he wants to play or not, I see it as a chance to spend some quality time outside having fun with dad. I find it’s easier to get him to open up about his day when he is out doing something he enjoys, and if nothing else, hopefully he’ll look back fondly on those times long after I’m gone.