Shall I give the reference list?

I need some advice.

I’m currently working for an auto company under 10km away from home. Like all other people in auto industry, we are struggling in this economic downturn. A few weeks ago, a HR in health care industry found me and I went for 3 interviews. Company is growing. But pay is down by 10K and mostly, it’s far from home – about 40KM one way on a jammed highway. I have a 10- year- old needs to take care. I asked for flexible hour on the interview. They haven’t given me an answer, but they are now asking for my reference. Can I ask for a conditional offer with detailed term of employment before giving them reference list?

Thanks in advance!