I also have serious reservations with her and Abe dating as she is also dating two other men and refuses to tell either of them about each other or Abe.
So he does not want you to be honest with her.
She is not honest with her other partners.
Why are YOU dating Abe?
You seem to want honest in your relationships -- he's not delivering. Neither is she.
I have to agree with snowmelt -- maybe you need to step away?