Well I can't speak for your state, but here in Oregon, I was able to get into school just fine but had to talk to the director a few weeks into the program. She wanted to let me know that I might run into problems when I applied to the board for my license but that I was allowed to continue if I wanted to (mine were 9 and 14 years old at that time). She never mentioned anything about liability insurance for students so we either didn't need it or I was eligible, I don't know anything about that. Of course I decided to stay and my experience with the board was that I would only be able to get a license if it was granted on probation. I agreed to the probation stipulations and have been licensed for a few months now. I've had about 4 interviews so far (since October) and have another one set up for next week, so you can get companies interested in you, you just have to start looking at the right ones.
Here's my advice for you...first, I would ask your program director if the insurance is the school's policy or the hospital sites' policies. If its just the school doing that, then you should find another school to go to (easier said than done, I know but if you can get into one school, yo have a good chance of getting into another, right?). Also, you said you were writing a reconsideration letter, is that like an appeal of the decision? If so, consider what you have done since that last DUI 3.5 years ago...have you been in recovery or just sober? Would the school allow you to delay your start date to another time, maybe 6-12 months later if you were willing to start attending meetings/submitting voluntary U/As? I would have another meeting with the director and ask if there is anything you can do to be eligible for that insurance, in fact, find out who the insurer is and call them yourself.
I was told by my director (who had been told by the head of the board), that the literature says that after 2 years of recovery, the incidents of relapse are significantly lowered so this is the time frame that I have found to be the "standard" both with the board and with employers. So I don't think its the time frame...not knowing anything about you though, it would be hard to tell why they aren't more willing to work with you right now.
If you want to talk more, send me a private message and I'm happy to give you whatever advice I can
Its not an easy road but I can tell you that after having gone through all of this, I am more committed to my recovery and my career...I've had to work harder for it than most of my peers. I also know that recovery and change are possible and have honestly made me a much more understanding and empathetic nurse, especially in the field of addition.