I'm planning on having a birthday party. I'd like to invite a friend of mine, however, nobody in our group likes his girlfriend. Is there a polite way of hinting I don't want her there? Chances are that she might show up with him anyway even if she's not invited.
Try viewing the situation in a broader context. It's not really just about this birthday party, after all. If your friend is in a long-term relationship, this is going to come up every time your group wants to go to a movie or have a party or have dinner out or whatever.
I have a friend I've known for 30 years. A few years into our friendship he started dating somebody who I and several other friends dislike. They're still together (married now), so we're stuck with her if we want him. But -- not all the time.
Members of a couple don't always have the same interests. My friend likes board games way more than his wife does, so when we're getting together for a day of gaming we invite him, not them, and that's ok. On the other hand, something like a birthday party is a "general" activity, not usually tied to specific interests, so we invite both of them to those kinds of gatherings. I've found that larger parties are ideal for this -- you can get your "included the distasteful spouse" points while diluting the effect. The more people there are in attendance, the less time you usually spend around any one of them. Sometimes you can get it down to "hello", "may I take your coat?", and "thanks for coming".
To increase your chances of enjoying your party despite this person's attendance, try to invite other people she'll like spending time with. I call this tactical party-planning. When I'm planning a gathering I usually have the set of people I know I'm going to invite and then a larger set of people I'd like to invite if I can (depending on space, money, or whatever constrains the overall size). As a host I don't want any guest to feel isolated, so "has common interests with so-and-so who will be there" can act as a differentiator when selecting among that larger set.
To go back to your original question: for the birthday party, assuming it's not some small and intimate gathering, I recommend just gritting your teeth and inviting both of them, and if you can invite some others who might enjoy talking with her, do that. For get-togethers with your friend in general, try to identify some "just us" get-togethers. Excluding your friend's girlfriend from everything won't work, but having some things you do with him and some things you do with them is doable -- and that way you don't force your friend to choose between his friends and his girlfriend. That rarely ends well.
There is no polite way to say this as it is an incredibly rude gesture. The underlying problem seems to be that you do not trust your friend's judgement in women. You could go with the honest approach though:
Hey ___, I know you like your girlfriend, but I do not and I have no interest in getting to know her better. The party is for ____ and we feel that it would be better if she were not there.
Be prepared to lose this friend, but it sounds like you are already at risk of losing the friend by forcing him to choose between you and her.
There's no polite way of "hinting" anything. You're going to have to deal with the problem head on, and hope for the best.
Just tell your friend the truth: "We all like you, but none of us likes your girlfriend," and that he'd be much more welcome at the party than her.
This "puts the ball back in his court," and can also lead to a "separation" of the following two cases.
One of two situations is likely to be the case:
1) The girlfriend is "poisonous," and "everyone" knows except your friend. If that's the case, he'll find out soon enough. You may "lose" your friend for a time, but when he figures out why people are behaving the way they do, he'll come around. Just keep re-iterating "we all like you, we just don't like her." Welcome him back when he comes to this realization on his own.
2) The girlfriend is "okay,"(to an objective third party observer), and there is something wrong with your group. They dislike her for the "wrong" reasons (dissimilar backgrounds, lack of coolness, etc.). If that's the case, be prepared to lose your friend. Otherwise, you may have to make a decision or choice to be friends with your one friend (and his girlfriend), or "all but one." If you want to keep a bridge to him, you might admit that you "might" be wrong about his girlfriend.
Assuming your friend's girlfriend is known to be toxic, always take the high road. Never criticize his girlfriend or try to convince him that she's toxic. This will only make him defensive of her. Trying to drive a wedge between him and her is like telling a smoker they should quit. The smoker may realize it is bad for their health, but they're still unwilling to part with their comfort. Invite her to the party and treat her like you would any other good friend. If she "ruins" the party or acts in a toxic manner while you and other party goers are treating her fairly, your friend will have nobody to blame but her for any drama caused. Without a scapegoat, he'll be more likely to consider the negatives of his relationship with her.
Every humiliation from the scenes she causes without any sign of provocation will drive these negatives home and once they outweigh the benefits and other options (introducing him to other female acquaintances) will likely seal the deal.
Yes, it's called a "guy's night". Many of my friends have leveraged this. Or "girl's night".
Alternatively you can invite her last minute or in some roundabout way "oh, yeah, she can come". If none of your friends like her they will probably ignore her and she will feel left out of the group and become less likely to come out. Just be prepared for him not to come out as much either.
Option three would be to wait it out. If there is a consensus on distaste for her, the relationship may not last long. His girlfriend may eventually come to reciprocate your distaste for her and likely will stop wanting to go out with him to see his friends. When he goes out to hang with you alone, or doesn't go out period, it puts a strain on the relationship.
Background: best friend of over 20 years dated two of my ex-girlfriends. We're still friends. Women are gone.