Ok, no moral questions asked. But remember one thing: seems to me like you want a LTR. Lets say you get there.. if she hooked up with you while she was in one, she will do it again when a skilled enough pua comes along (no, you are not that special).
ok, but lets cut to the chase. You need to be better than her bf. She will compare her options and staying with her current bf is easier, so you really need to outperform him. Also, no relationship is perfect, get her to
focus on the things that are wrong in her relationship.
If she tells you he doesnt do the dishes, tell her a story about you or a friend of yours, who's bf/gf had a very similar habit and how it eventually drove them apart. Stories work always, just make them sound good, if you need help, post some of the problems they've had and I'll make you a story

The idea of stories is to make her see that even though it might not seem big at the moment, it will eventually become a dealbreaker.
As a bonus telling her a story tells her that you understand her feelings and what she is going trough, something that very few men do, but almost all women value highly!
Also be careful, don't turn into a wussy, you are NOT a second bf, let her bf do the wussying, at a certain point, it will turn against him. At some point you can play the "I can't do this anymore card". This has to happen at a point where everything between you two seems perfect, then tell her your consciousness can't take it and that you think you shouldn't be in contact anynmore.. if played right, she will understand it, but.. wait a week.. she will break and contact you. Thats the tipping point, be smooth but absolute.