The only concern I have is that if she goes back to Vietnam before the child is born, that it will be much more difficult to obtain custody.

I do understand that pregnancy can cause moodiness, but I don't think it justifies silent treatment for hours at end, and acting like a child instead of an adult. 

Honestly, I don't think anyone is worth the stress and difficulty that she is putting me through right now, and yes, we wouldn't be seeing each other if she wasn't pregnant. Obviously, her pregnancy changes things drastically, and I am more than willing to put 110% effort into making a relationship work, whether it be romantic, friendship, etc, as any decision I make is not just about me anymore, it is about my child. 

All this being said, I am wondering if it is worth ending things and just leaving her to be a single mum back in Vietnam. I know that it would make my life easier, and I don't think that knowing I have a kid out there would necessarily eat me up inside like it would for other people. My family would be very upset with me, but they can be rational and I am sure that they would understand in the end.