I think the most important thing is to demonstrate changed circumstances. If they (the council) think that you're still experiencing the same problems, they may not want to let you continue. But if you can convince them that those problems are in the past, and you now know what it takes to succeed in law school, well...you may have a shot.
You should be as specific as possible, don't speak in generalities. Say exactly what has changed which makes you confident that you can succeed. Give specific examples, and be positive. I wouldn't spend any time at all blaming a lack of IRAC instruction, or the curve, or spring admissions.
Also, be 100% honest even when it hurts.
Remember, the council wants to be reassured that you're a good bet. Focus on the positive aspects, and show that you have a plan for success.
BTW, I went to law school with kids (and a job) too. It's an unbelievable grind, but it's worth it. I did well the first semester and had good grades. Even so, I considered dropping out because it was so much stress on my family. Now have a job that I love, and am thankful everyday that I stuck it out. Feel free to PM me if you have any questions. Good Luck!