A) Getting full custody is a SLICK SLOPE homey. That should be a plan "c" and should be done "over time" - bulding a "paper trail" of evidence to present to the court. And REAL evidence, not "well I heard that she smokes pot" - but more like "here is a public police record of her going to jail for smoking pot multiple times." Not "she sucks with money" - but "here are financial records of the accounts that we have shared" or "here are receipts from me getting her lights turned back on bc she is not financially stable." Not "I heard that she can't get to work on time", but "here is proof from her last 3 jobs that she was terminated from due to her inabilty to get to work on time due to no transportation" - etc.
2 - You DO NOT want the court into your personal life unless there is NO other way. The system is BROKE, and always will be. The court wasn't there when yall were f*ckin' and why women (mostly) and men choose to go that route is beyond me. BE AN ADULT about it. You talked things out before - talk them out now.
X - I'd be kinda suspicious about her not telling you until you told her that you were engaged - that's a little fishy. I mean 5 months b4 you found out?? What was her plan b4 she knew that you were engaged, to not tell you at all?? Her "mom" is hardly proof that it is yours. The kid has rights to know who her father is (and not b/c her mom SAID so, but b/c DNA proves it) and if money is gonna be coming out of YOUR pocket - then you deserve to be 100% sure as well. DO NOT - I repeat - DO NOT sign the birth certificate until paternity is proven or you just f*cked youself in the a$S HARD (ask me how I know).
26) Like QD says - good luck (lawyers, yes, a good thing)