First of all, you have to get the both of them out of the room from each other period. I have 2 girls that share a room, but they are 3 and 1 so they do very well. You cannot stick a 9 month old screaming child in the same room as your 3 year old. Once the 3 year old gets up, she will continue to think it's ok to sleep in mommys bed and she won't ever get out of that stage. So you have to stop that now!
As for your 9 month old getting up every 2-3 hours, I would suggest trying formula w/ cereal right before bedtime. The formula will coat the stomach better and the cereal will stick. Make sure she isn't getting gased or has an acid reflux problem. You can even try putting the mattress up about 6" where her head is. If it is gas or acid reflux, this helps so the burning doesn't go up and hurt their tummies.
As for your pediatrician, he/she must not be very good. My pediatrician would be checking her over and doing tests to be sure everything is ok. Has she done this 2-3 hours waking up every night since she was born? Or did she sleep good and then now she is all of a sudden she is getting up? If she's done it since she was born, then yes, you may need to just continue to let her cry it out. If she is just starting it, there could be several other things going on. I would suggest maybe a new pediatrician.
Now, I know your basement is finished, but you cannot stick a screaming 9 month old in a huge room by herself with nobody near her. If there is something seriously wrong or she starts choking and you don't hear it, then what? I know it's hard since you aren't getting much sleep but I would be checking with other doctors to see what the problem is. It really sounds to me like she is doing it on purpose though. She knows that she shares a room with her sister and knows that you'll come in and get her. So the real question is, when you get her, does she stop crying immediately or does she continue to cry until you feed her?
If she stops crying when you pick her up, then you know that she is doing it so she can get your attention. If she is continuing to cry until you feed her, it could be that she is going through a growth spurt or that she is gased.
There are so many factors here that you have to consider, but you have to be patient with kids. Just please don't stick her in the basement by herself. She is only 9 months old! Eventually she will sleep and so will you.......and your 3 year old!