I am currently the homeschooling mom of my two daughters ages 15 and 10. I actually got started by talking to a mom who had a diabled child much like yours. She and I both agreed that being able to help your child learn at THEIR pace and in ways they can best work, is one of the best benefits of homeschooling. As mentioned before, Indiana is one of the easiest states as far as recording. Really the only reason you should register is because of pulling her out of a public system...this way she won't be truant. By notifying the Dept. of Education, you should be fine.
I will warn you that once you get into finding cirriculumn to use, it can be overwhelming. You might want to just use what she's been using in the public school, or find one that you find easy to use. In the spring, the Indiana Home Educators Association holds their annual convention. Besides workshops and lectures, they have an exhibition hall with TONS of supplies, cirriculum, etc. Again, it can be overwhelming, but it can give you a great idea of what is out there. THere are also used book sellers too which can save you lots of money. Here's their website: www.inhomeeducators.org.
Also, some a websearch of home school materials and you'll find tons of individual websites.
One thing I want to point out about homeschooling. You'll get a lot of opinions about it. I know you can do it if you want to and you can find a system that works for you. Every home school in unique. Some people set up a special room and it's just like a classroom and they work in a certain time frame, etc. Some are more lax. Some people work well within a homeschool group where many people can pool their efforts, and others tend to work individually. That is the beauty of it. My objective is to encourage my girls to do as much on their own as possible as to teach them HOW to learn....but providing the resources they need. They are very independant workers, so it works well for us. Also, I let them create a setting that they feel is best for them to work in. One likes to spread out on her bed. The other one works at a desk part of the time, but curls up on the couch to do her reading. Each child has their own learning style, as you've already discovered. Don't be afraid to try something new and adapt it to work for you and your daughter. I think most moms agree that TV and radio can be a distraction and should be limited.
As far as doing something different with your two children, I would not be worried about leaving one in public school and the other one at home. My friend I mentioned before did this and it was fine. In fact, if the one really enjoys and thrives in public school, it might cause resentment to pull him out. In my opinion, homeschooling is just another option. And, I'm all for doing whatever is best for the child to learn and get the best education possible. We are all different, so let your children be different.
Lastly....sorry, this is so long!!....people have a lot of opinions about public and home schooling. You know your children best. Don't be afraid of doing what YOU think is best for them. Most of the arguements against home education is just not founded. However, public education isn't all bad either. I had some wonderful teachers...some of them were also great Christians and taught good morals as well. But, homeschooling does give freedom to learn and grow much differenly than public school, so it's hard to compare sometimes. But, don't be afraid.
And, if you are discouraged...CALL ME!! LOL Just like anything else, you'll need encouragment along the way. I'd be happy to help you in anyway I can.
Good luck!!