Here's another way of looking at his golf club. He carries it around to make him appear more intimidating. It helps him exert power over others. It is his tool of intimidation. The first thing he does when he gets home is call for Lorraine and place it in the bag. Normally, he does not need his golf club when he interacts with Lorraine. She is intimidated by him without it. Until now. Lorraine is fighting back. Lorraine has found her own tool (Gene) and she's wielding it against Adam BIG TIME! Lorraine's new tool has cast him from his home, and he was cast out without his club. He is now weak against the world, and it is at her hands that he finds himself 'broken' (like a horse).
Gene is a part of Lorraine's psyche who, after Lorraine had been oppressed for so long, fights back against the oppressor (Adam) and wins. And Lorraine, with this new tool, renders her oppressor powerless. Not only powerless over her, but against anyone else in the world (he is now in the world without his club). Gene is much like one's "Hero" archetype.
She gets the 'pool guy' and he gets the pool. Lorraine has acquired a new tool that is very valuable. A tool that gives her the ability to fight those who wish to oppress her in some way. The pool is just that...a pool. In the whole scheme of things, the pool is worthless.
Lorraine is representing someone...and I think it's Diane.
Let's go a step farther. Most will agree that the golf club is also phallic in nature. The golf club plays a duel role. What is Adam missing, then, now that he has been expelled into the world without his 'power tool'? Both his power and his penis? We don't know what Adam did to Lorraine, but the fact that Gene is found in Adam's bed is possibly a clue.
It is my opinion that someone had their penis cut off. This would be why Adam is powerless in the world. He will not be able to use his penis to oppress anyone else, not just Lorraine.
If Lorraine represents Diane, then who does Adam represent? It's possible that he represents himself. That he is a real person in Diane's life. A person she wishes she could 'castrate'...or someone that she did castrate? Anyway, we do see Betty with a knife while she practices those lines with Rita. Those lines that suggest inappropriate sexual behavior.
One more thing: Gene says "He's probably upset, Lorraine."
Why is Adam upset? He is upset because the acquisition of Gene represents Lorraine's intention of fighting back. She is 'playing' with the idea, and he sees that. This is what pisses Adam off, and he tries to get back at her (or stop her) by 'pouring paint on her jewelry'. The paint scene is representative of a last ditch attempt by Adam to 'beat her down' and make her rethink the notion to fight back. When they are wrestling on the counter, she calls Gene's name. This represents her 'calling on', or utilizing, her ability to fight back.
What he did to her, what the 'pouring pink paint on her jewelry' means, I don't know yet...but it's possible that he injured her in such a way that she cannot bear children any longer (destroyed her jewels). And what we see next, Adam being thrown into the world without his golf club, shows us that she returned the favor.