I think that your girlfriend is dealing with a very stressful situation with her mother, and it doesn't sound like you were able to support her (although I get the sense you wanted to). If she is tense and volatile, she could very well blow up at inopportune moments.
As far as the situation between your girlfriend and the ex, it boils down to trust. Do you trust her to stay committed to you? If you have doubts, you need to end it: it will eat at you otherwise. Also, as you said, her ex is her best friend: that's a relationship that you have to make peace with for yourself. If you can't(due to jealousy) this is bound to fail, since you would require her to break contact with her best friend, all for the girl she sees a couple of months a year. She'll resent you for that, for sure.
If you have faith in her, let it go: don't stress her out over this situation with her best friend, but rather be supportive as far as her mother goes.
And next time you make arrangements to meet with your gf, make sure she has the time for you that you deserve, in so far as that you are her significant other and you flew over to her to see her.