Step 1: Make her prove to you she's pregnant. She's lied to you about the pills (It's true, sure you could forget a day of two, but an entire week? No.) If the test is negative, drop the *****. If positive, proceed to step 2.
Step 2: You're not going to convince her to get rid of the baby. As much as I may hold her in contempt, she obviously wants a baby, and no one can, within their legal rights, deprive her of that.
Step 3: For 9 months of sheer agony and prenatal care (sometimes including hormones), she will be thrown into a hormone induced rage. Shortly after, she will be flooded with, you guessed it, more hormones, and she will begin to develop a maternal attachment to the baby. You, as the potential father, should make to effort the aid in whatever way appears suitable.
Step 4: Determine that the newborn (as I'm sure you've noticed, I've skipped a little bit) is actually your child. I will not pretend that the following statement is based in fact, as I do not know this...woman...but she seems like the type to sleep around. If the infant is not yours, go on your merry way a little bit more cynical, but somehow wiser, than before. If it is your child: pay up. I'm not saying you have to father the thing, but what you do have to do is support this woman in her own efforts. You've already made it clear that you are OK with paying child support, so hopefully, this is not a difficult step. However, when you decided to trust that she'd been taking birth control, you made a decision. You knew the risks of unprotected intercourse, and you were aware of a means of preventing pregnancy. True, the first time may have...well, we'll say "caught you by surprise", but the second time. Well that, that was just naive. ( Stupid umlaut.)
The reason I say this is because I've learned that NEVER should you trust another person to handle contraception and the like on their own. Even if that person is well-meaning, that doesn't mean they're not forgetful. In this situation, you are both responsible. True, she may have been the one behind the actual conception, but you allowed it to happen. You were present during the act, and are not an amnesiac.
Now, this is just my opinion, and being completely honest, it's fantastically uneducated. I am not aware of the context under which many of the events you have stated occurred, nor am I any kind of refutable judge of this woman's alleged promiscuity. However, this is, in all honesty, what I consider to be the most advisable course of action. True, a community of internet nerds may not be the most capable advisers available to you, but this is what I've got.
Good luck, Sir. Though I don't necessarily agree with your status as the victim, the seriousness and pathos of your situation are not lost on me.
And I know, definitely TL

R material.