Such as, What things excite you sexually? Do you have to feel relaxed in order for the desire to flow? (and then the corollary to that question: What are some things that relax you?) Does reading erotica make you feel excited? Would using a sex toy for some serious stimulation help things out?
If she is drawing a blank, then maybe you can help refresh her memory. I know that when I do this with H, all of sudden he is coming up with things that turn him on. (not that he ever DOES those things, lol, but that's a different topic)
I think as long as you continue to accept her "I don't know" answer, you will continue to get it. Maybe a little gentle prodding will get her thinking in another direction and she will realize that her avoidance tactic won't work any longer.
As far as her "involvement in the family" response...well, my H sometimes says things like this too. It used to infuriate me until I realized that he VERY easily gets mixed up as to what we are really talking about. She might be wanting to guide the conversation back to "what can I do differently to show you I love you?" rather than "What can I do differently to arouse you?" My H does this nearly every time we talk about sex. He wants to turn it back to love for some reason. Next time she says that maybe you could ask her to clarify what she means by that: That you being involved with the family makes her HORNY? Or makes her feel secure? Or what does she mean by that? And if it's anything other than horny, I would gently but firmly redirect the conversation back to sex, since that is what you are trying to work through after all.
Hey I just thought of something. Maybe my H does that (turn it to love) because when I am pushing the sex issue he suddenly feels insecure and sends out a "bid" to make sure that I still love him as much as ever. That makes perfect sense! However, he is still required to answer the hard questions and if he doesn't know, then I set a time for him to think about it and get back with me. If he hasn't gotten back with me in the time frame we agreed on, then I ask him again. I know I sound perfectly horrendous to live with and I promise you in NO other area of our lives am I this aggressive, but dang, I have to be this way! Otherwise I would have heard "I don't know" about a zillion times and never gotten any farther than that.
