Here is an easy rule of thumb in that situation: If W offers me ANY time to spend with my kids, I take it. I don't care if she's gonna sleep with 14 men, and run naked around the park with her hair on fire. Worst case, you will be a hero to your kids, and show her what a good dad you are - I can think of worse things than that!
Otherwise, I don't think it was a mistake to require that she make the decision, but be firm about it, don't talk about it ad nauseum. Tell her: "Call me back with whatever you decide."
However, Coach is right about many wives wanting someone to lead - my W is very strong-willed and very in charge, but when the poopie hits the fan, the first thing she does is call me. If it has to do with my kids, I address the situation, and I take action.
If it has to do with her having a hard day at work, or not having any money, I sympathize appropriately, i.e. "It must be really hard with balancing school and work, I can't imagine." Then, I find some reason to go. W has decided not to be my wife, so she doesn't get husband privileges.
I know that many on here take it as a good sign when their spouse calls with problems, but I guarantee 90% of the time it is cake-eating. My W is with a complete loser, and she knows it, but anytime the really hard stuff hits, she doesn't call him, she calls me, because she knows that I can handle it, and OM wouldn't.
So when it happens, be strong, and firm. Do not attempt to control - don't tell her what she should do. You can choose which things make sense to get involved in. My W called me and said she needed to get new tires - hers were completely bald, I mean down to the bare rubber. My kids ride in her car, so it was in my interest to assist. I knew she had no clue, so I looked up a phone number for her, and suggested she get price comparisons. I didn't tell her to get them changed, or how to do it, or where to go.
Another time, she called me, and had hurt her back. I inquired as to whether she was OK or not, and after she said she was, I didn't say anything else. She started talking about how she might lose her job if it didn't heal fast enough, and money was tight - this is a situation that she brought on herself, so I listened. I didn't offer up solutions, I didn't offer money, I simply said mm-hmm. I waited until she was done, told her I hoped she felt better soon, and gave a reason to disconnect the phone.
I realize I'm not addressing your specific question - but I don't know your wife, or the specific situation, or how you relate to your kids, so I'm sticking with generalities. I think the best place to show firm strong leadership is with your own life - exercise, health, career, spirituality (if applicable) - and even more importantly with your kids. If she wants you to take the kids, and you possibly can, do it - don't use the kids to create a burden on her.
