Don't ignore her in front of your friends. Part of growing up and being a good boyfriend, as well as being a good son and friend, is learning that you can't always get what you want. If you have to be honest about something you wish she did or didn't do, tell her in a kind and sympathetic way so she doesn't get mad at you.
But whether you want to move a little further than kissing or to go all the way, you have to make sure that your girlfriend is completely ready to take this step. Just shower regularly, shave if that's what you normally do, and wear flattering, well-fitting, and unwrinkled clothes. While your daughter is, predictably, aghast when you show your face in the same room as her and her boyfriend, it would feel even stranger to her if you granted her free reign.
It's important to be attentive and support your significant other's goals, but try to recognize when they need personal space so you can provide that, too. If you think your girlfriend is starting a lot of fights, communicate about why this is happening and how it can be changed.