Hi Ken.
Welcome to WGT.
On reading your post I'm a little confused about a couple of things. Firstly WGT is free to download and play, so you shouldn't have needed to purchase the game itself. There can be ongoing purchases within the game (e.g. upgraded balls and clubs etc.) but at its most basic level the game is entirely free.
Secondly, the game can be played on PC/Mac etc using a keyboard and mouse or touchscreen, or on mobile. Someone will correct me if I'm wrong but I don't think using a controller is possible, depending upon what you mean by a "stick".
But to address your query, each person playing WGT needs to have their own account to create their own player profile. And WGT's Terms & Conditions state that only one account is allowed per person. While it's perfectly possible to have several different accounts within the same household each person would need to be playing on a different device for a multiplayer game, as you cannot have more than one person signed in on an individual device at a time.
I hope that helps a bit, and as I said if I'm wrong about any of this I will swiftly be corrected below.
I hope you can get something worked out to play with your kids.
Nigel.