No divorce exists in the eyes of God as far as the catholic church is concerned since that would imply God made a mistake. You can get an annulment only, and the one person I know that got one said it took over a year and it involved going to a number of meetings with various people in the church to explain the reasons. Not saying it can't be done, just so you know it can be a bigger time (and emotional) investment than getting the paperwork from the state done.
On a more down to Earth level, I have to agree with cautions given. I was terrible with women in my early life and I recognize the willingness to change things about yourself in order to be with her this early in the relationship. It all came from my own insecurity and eagerness to have a relationship, both of which aren't emotionally healthy and likely to drive her away eventually and in any case are a shoddy foundation.
For there to be any sort of real relationship, both partners' emotional investment in the relationship has to be roughly equal, and while she is still married and living with her husband her emotional investment is always going to be limited. Now if (like others have said) you just want to have some sex and can keep your long term expectations in check that's great, but for there to be any chance of a real relationship progress on this divorce needs to be forthcoming in the short term and it needs to be measured in actions, not words. Otherwise your relationship with her is going to plateau and fizzle out, best case in that situation is you have a semi-regular friends with benefits situation, worst case situation you end up wasting months/years waiting for a level of relationship that is just not going to happen.
I'd consider the scenario that this woman just wants to get pregnant again (she's under significant time pressure if she's early 40s) and will end up staying with her husband when she does. Don't underestimate what some women will do in order to have a child, plenty of dudes get suckered into a relationship only to get ushered out the door once the kid is born or on the way. Women aren't all princesses that do no wrong and (like men) can talk themselves into all sorts of fucked up shit.
