Hey! First off, CONGRATS on starting! I know first hand what it can be like when people you love and care about don't support you, or worse, think you are crazy for trying, but PLEASE remember....you are doing this for you, and your daughter is going to see how strong and healthy her mom is when you do this workout! It will effect how she sees her choices too, and you are setting such a good role model for her whether she knows it right now or not. ;)
If your sister has the book or nutrition guides for Slim in 6 I would go ahead and look over them. I also like to write out my workouts somewhere even if it's on a free printable calendar. It helps me know what workout I have to do that day, and I also make them off to see my progress. If she doesn't have the nutrition guide, I would recommend asking your coach about calculating your calories and getting some meal ideas. If you don't know your coach or can't get in touch with them, just let me know and I can send you some of my meal plans and help you figure your calories.

What are your goals for slim in 6?
Slim in 6 is a beginners workout, but I would modify the core movements because of your spine. By modify I mean just do what feels tough but not to the point of discomfort or pain. You aren't working out for a week or a month....you are working out for your LIFE so do what you can now and know you will get through every move soon and then move on to something even tougher! ;)
Is your sister going to be your accountability partner? I noticed from your bio you have a lot going on, and I know that can make it tough to stay accountable! I JUST finished school and i know the last semesters can be a booger! lol! What are you studying? If you need anything at all or if you (and your sister if she wants) would like an accountability group i am in a great one! we share meal plans, tips, recipes, progress, questions, motivation, etc and it's free. Would that be something you'd like?
I hope i've helped...just remember, you are doing this for YOU. When someone starts something AMAZING others may not get it off the bat, but that doesn't mean they don't succeed or get their support eventually. You do this for you and we'll be here to back you up and help you!