Hey I'm a nurse too. I work three 12 night shifts, but usually schedule myself 2 days on and 2 off (I feel sorry for your rotating schedule!). I've done P90x and Insanity this year on my schedule. I also just started TurboFire last week
I do my workouts BEFORE work. I usually wake up around 4, start my workout, finish by 5, then get ready for work, then out of my house by 6PM. I have a boyfriend, I don't have kids, but I do have a dog that I need to take out for walks about 3 times a day. I just try to manage my time wisely on days I have work. I also have about a 20 minute commute to work.
If I'm too tired I just use the "rest day", and catch up the next day, but I try not to allow myself more than 1 rest day a week. It's tough but once you really get into it, working out just becomes a routine (like making a cup of coffee or taking a shower, you just do it). I've found that the first day on for work I have the most energy to work out, then the second night I'm more tired, so I may use it as my rest day.
I would suggest for your schedule:
Day Zero (day before you start work), work out
First day (1st dayshift), try your hardest to work out before or after work,
Second day day (2nd dayshift) count as a REST day,
Third day (your 24 hours off)-work out,
Fourth day (your 1st night shift) work out before work,
Fifth day (2nd night shift) work out before work again.
Sixth day (day after night shift) work out when you wake up again.
You could also use the easier or shorter workouts on days you have to work, so you dont have to use so much time.

Hope this helps!