Sorry I wrote a novel here, but I hope you'll read everything I wrote.

If you know for a fact there is something like psychological abuse going on (which is possible, IF she is persistently interfering with/deciding who he can interact with), then the best thing you can do is NOT to tell him what to do just like she might be doing, but to do the opposite: remind him he has choices.

Both in your words and in your actions (by setting an example in your own lives and by remaining available to him unlike the "friends" that you say dropped him), people close to anyone who unfortunately happens to be in an abusive relatinship have to consistently remind the person he can CHOOSE to talk to any loved one and that you will be ready at any time. (Make sure that's true by the way. The last thing he needs is to finally decide he's going to talk to someone and then the first thing out of that person's mouth is "I can't believe you dated someone like her" or "So you're finally getting rid of her," or something equally judgmental). If he has been hearing that kind of thing from anybody, regardless of how terrible she actually is, I wouldn't blame him for getting defensive.

Understand that IF she is abusive, what she is doing is slowly taking his belief that he has choices away. So the best thing you can do is jam that narrative up. Counteract it by reminding him how much choice he DOES have. Keep asking him to tell you all about how he's doing, what he's been up to lately, what he's doing for fun/that keeps him happy (i.e. use ways to remind him without saying so that no one should be dependent on having a partner to be happy-- think of it a bit like an advertising campaign or Inception or something-- you want him to believe it's his own idea what he does next and it's not just another person telling him what to do-- except that he does get to make his own choices and be proud of them). Keep generally checking up that he's living a full and happy life. If he isn't, then ASK him why he isn't happy or if there's anything he feels he's missing out on. Don't draw your own conclusions; ask questions about why he doesn't think he's happy (if he isn't).

If you think he's lying when he says he's happy, then he probably already knows it himself and just isn't ready to do anything about it yet. Short of him being in immediate danger, you have to TRUST him to come to his own conclusions that something's wrong. In the meantime, don't stop spending time with him just because he says no to the offer a couple of times. If he tells you that he doesn't want you to ask anymore, then be vulnerable and tell him you (presumably) feel hurt, and if he's not riled up, maybe ask why he doesn't want to spend time with you. Avoid letting him feel like the only reason you want to talk to him is to "pester" him about his girlfriend. Ask, don't tell.

Think of how you would feel if you believed you were happy in a romantic relationship yet all these people were "attacking" your choice of who to date. Any person in that situation is going to get at least a little defensive.

I still don't understand what difference you think ADHD would make. A trained therapist/psychologist wouldn't treat this kind of issue any differently just because someone happens to have ADHD.

Dealing with a higher than average level of hyperactivity/impulsivity/inattentiveness/forgetfulness/perseveration doesn't make you any less intelligent or perceptive or resourceful than others-- and yes that is what you are implying by insisting on tying ADHD to this.

ADHD can only affect relationships in ways that are related to ADHD. For example, people misunderstand your inattentiveness/forgetfulness/perseveration and think you don't care, or your impulsivity leads you to fail to hold back when you get emotional (be it joy, sadness, fear, rage), or people see how hyperactive you are and just plain avoid you out of second-hand embarrassment. These are things that can hurt and can shape a person's life somewhat, but those secondary aspects of hurt are not part of the ADHD! They are part of the lifetime of positive and negative experiences that ALL people build up in their lives. For example, a neurotypical person who happened to be bullied as a kid may find it shapes part of their outlook or some of the choices they make. Does that mean you can then go and assume that EVERYTHING the person does in his/her life is because they were/are being bullied?

Please remember that every symptom of ADHD is related to hyperactivity, and/or impulsivity, and/or inattentiveness, and/or forgetfulness, and/or perseveration. Leading researcher Dr. Russell Barkley is also adamant people with ADHD do not have their entire personalities or levels of ability defined by whichever combination of ADHD behaviours they happen to have. It is one of many layers of who we are and defines no one's behaviour entirely.

Anything beyond actual symptoms of ADHD is specific to that person's upbringing/life experience and/or possible comorbid disorders and not something just anybody with ADHD would be able to speak to.

So instead, I've spoken to this as someone who knows a few things about abusive relationships (in general), and how people who are trying to "help" sometimes fall into the trap of being judgmental, patronizing, or condescending, and thereby push away abuse victims. Further to that, I highly recommend you talk to groups for victims of abuse (as long as they aren't specifically groups for women victims of course). This forum has one here:
Survivors of Abuse - Forums at Psych Central
Perhaps you can respectfully ask the people in that section if you think what your cousin is going through sounds like abusive behaviour. You might have to give more details to be sure.

Though the verbal abuse I personally received wasn't from a romantic partner, I have been on both sides of this (including both as a not-so-effective but well-meaning advice giver and then eventually as someone who has hopefully learned a little now about making sure I am empowering the other person).

Further, if you haven't already, I highly recommend you take the time to absorb Brené Brown's videos on shame and vulnerability (all are on Youtube). Not just the most famous one but all of them. Read her books if you can. It will help you understand how and why people put up defences and don't open up.