I'd like to start by addressing your statement that your male puppy still squats like a female when peeing... That's completely normal as young males don't start lifting their legs until they're several months old. The fact that you don't know that tells me you're not all that experienced with dogs.
I also got the impression you're looking for this male dog to be on the 'macho' side, and that just doesn't happen simply because he's a male. Yes, some dogs are more 'macho' than others, but those dogs can get out of control & aggressive very easily, and you really don't want that.
On the peeing incidents...
I don't necessarily agree with all the opinions here, although I do fully agree with never 'beating' a dog. Jeez, I slapped my Lhasa on the butt once when she was young and the look she gave me about destroyed me, she was so deeply hurt - and she's not a submissive type at all. I never did that again. Now when I have to physically correct her for something I flick one finger on her butt, and I only do that when she's done something dangerous, like running out into the road after something even tho I'm telling her no, and she knows she's not supposed to be out there. She has an incredibly independent streak in her and deliberately *chooses* when to behave & not behave - and she doesn't respond to treat training. You can see her start to automatically do what I've told her, then she'll stop for a second, then go on to do what she wants to do. Fortunately, she only does that once in a while, and she's a perfectly well behaved and wonderful dog all the rest of the time.
I would've interpreted the first time your dog peed as a territorial mark, or a reaction to a perceived loss of your attention to this other person. It's very possible your dog is insecure if you haven't known how to handle him properly. After taking him outside I would've brought him back in and made a big fuss of paying attention to both your girlfriend and him at the same time, and having your girlfriend do the same thing, so that he knows he's included and becomes secure with the situation.
The second time he did it, right after coming back in, I would've interpreted as rebellion. I would've told him 'no' and leashed him across the room from me for about 10 minutes. Then I would've released him to see what happens next. If he did it again, back on the leash. If he didn't, make sure you pay attention to him the same time you're paying attention to your girlfriend.