Miss Kitty, I can't think of any additional suggestions beyond what has been mentioned here, and I am not a nurse or a nite shifter, but I am a single mom and I wanted to offer you encouragement and tell you to have faith. I don't know if you're a spiritual person or not but I'll tell you my story and how it's an example of God truly being able to work miracles.
As I said, I'm a single mom, and like you, I had no idea how I would make it happen, but I applied for every shift I could at the local hospital back when i was trying to get my first CNA position. I had no experience and the hospital required at least 6 months. I didn't know who would watch my child if I got anything other than a day position, but i figured I'd cross that bridge if I was ever fortunate enough to come to it. Turns out, as soon as I finished my CNA class and got certified, I landed an interview for a hospital tech job. Prayer answered! The bummer was that it was for the nite shift. I didn't know how I'd make it work but I was determined and had faith that everything would somehow work out. So I went to the interview, spent an hour or so interviewing with the staff, and sat there wondering the whole time how on earth would I possibly make this work if I got the job. They really liked me, I liked them, and I knew I had a real chance at getting hired. Lo and behold, at the end of the interview, the manager tells me that he just got notice that day from one of his day shift techs that she's leaving, and none of the nite techs want to move to day shift, so he's now needing a day shifter as well. He asked if I'd prefer days or nites if I were hired. Of course I told him days, but also said I'd be open to either or. A few days later I got a call offering me the day shift in that hospital.
Sorry for being so long, but I said all of that to say, Miss Kitty, just have faith. It will all work out. It may not be easy, you may end up going on a different path than you originally set out, but you never know how wonderful things may end up in your life. Just let God do His work, and go with the flow. Most importantly, and I cannot say this enough, trust your gut! You and your family are in my prayers!