understatement of the month

If OP, in OP's words, "upset" his GF's mother, I don't see why the mother would be a problem. It sounds like OP's upsetting behaviour is the problem. It seems to me that the GF finds such behaviour to be a complete turn-off. Should she have sex with him even if she doesn't feel like it? I don't see that it's "controlling" to say no when you're not in the mood.

It's controlling to be mad that he hasn't recognized that it's a deliberate "sex ban" and punishment. It's not that she's just not in the mood. It's that she's deliberately withholding affection as an attempt at punishment and then mad that he's not recognizing it. She's definitely more than a little passive aggressive and toxic. We can't promise that the OP isn't also toxic and at fault, but the girlfriend's behavior is also unreasonable.

Yeah, then she will just stop having sex period, and you're stuck with her.

A child who grows up in an environment devoid of affection is being abused, sure, but here I get the impression OP is grown man. The GF doesn't find her BF a turn-on when he upsets her mother. She is not withholding affection, she doesn't actually feel any affection because she thinks he's a jerk. The use of the word "upset" kind of implies that he was in the wrong. And the months-long dry spells were perhaps caused by other jerky stuff he did. Refusing to have sex with someone because you're not in the mood after your partner has been a jerk is not controlling. It's about exercising one's free will. There's this thing called consent that's been trending for a while you know? Of course if it lasts for months, it could also mean that she's not very hot for OP in general, maybe he needs to learn to turn her on better. He could start by behaving diplomatically with her friends and relatives (which shouldn't have to be stipulated but here we are), and make sure to give her a good time before coming himself. Or he could get out and get himself another GF who doesn't mind if he upsets her mother. Good luck with that.

The inability to resolve issues, the lack of clear communication and the withholding are all red flags on her side. She's clearly showing toxic communication, relationship and problem solving strategies. That doesn't mean that OP isn't also part of the problem since we don't know how he is acting, and he's likely also part of the problem, but as I see it, she's showing a lot of the "four horseman" signs of behavior in a relation, especially withholding affection and stonewalling. Those are toxic behaviors. Also it doesn't seem like "she's just not interested." She openly admits it's a deliberate attempt at punishment. If they've had months long spells, they've been in this relationship for a long time, and may even be living together. If they have kids, are living together or otherwise highly invested in the relationship and want to stay together, couples counseling is probably necessary. If none of those things are true, I think the writing is on the wall to jettison this failed or failing relationship, and take and learn lessons for the next one.

If that's the case, the girlfriend has the responsibility to address and communicate her feelings and not just shut OP out. As it stands, if this is a regular thing, it's a very toxic pattern to the relationship, on both sides.

I agree that they need to talk this through. But, you think refusing to have sex is bad behaviour? Her feelings don't count? When he's upset her mother? That doesn't count as bad behaviour? Wow. If my partner was rude to my mother, for example, I wouldn't feel hot for him.