Dating, having sex, being in love, and all that other garbage is all well and good when you're 13. But attempting to raise a family when you're 13 with your 13 year old boyfriend ISN'T okay at all. Being that young there could be MAJOR birthing complications, and if your friend won't allow his chicky-poo to have an abortion then he obviously doesn't care about her as much as he says he does.
I'm not sure what it's like everywhere else, but here you can't legally work without parental consent until you're 16, so little boy + little girl + baby + no fucking money or jobs = really shitty situation. Since there's no way either of them can survive on their own, then it's irresponsible to even THINK of attempting to raise a baby.
At the very lease she will have to tell her parents and admit that she made a mistake, she should also mention that she took precautions... that should win her some brownie points. It's almost better that her mother is all for abortion, considering that the alternatives are kicking her out with a baby, or forcing her to raise the baby in her house and resenting her for it.
If they're both against abortions then the best choice for everyone may be to carry out the pregnancy and give the baby up for adoption, at least that way the baby will have a chance at a life that isn't absolute crap.