I wonder if the Illustrator file was in RGB color mode?
At any rate, it sounds like way too many steps are being taken to reach the same place.
"I am using CS5 and created a swatch pallette in InDesign (all RBG values as the photographic printer I outsource to uses RBG). I tested all my colors with the printer and they were spot on (using a file created solely in InDesign). I saved the swatches to a .ase swatch library so I could access it from Illustrator. In AI, I created my design, then placed it in InDesign"
This appears to be OK method. Double check your application Color Settings and make sure they match. I was not aware that InDesign was an RGB color space application. As I understand it, you can apply RGB color to a CMYK document.
"Then I created a press-quality PDF which I opened in Photoshop at 250 dpi so I can create my high-res jpeg for printing."
I'm pretty sure you do not have to use "Press Quality" if you are setting up your business for output on a photographic printer. The PDF may have converted your color to CMYK, unless you instructed the application that creates the PDF to "Leave Color Unchanged". Not sure why you are going to .jpg unless you are trying to keep system resources to a bare minimum. And, it sounds like you have no RIP in your process. The PDF should be enough for output. Your PDF should be a standard 150ppi file for inkjet output.
"The problem is that the colors are different between InDesign and the placed Illustrator graphics. I looked at some of the swatches in Illustrator and the RBG values are different than in InDesign! Color management is not my strong suit, so I'm hoping for some help here. I'm about to launch a new business and need to have the colors be spot on. I have printed color charts for my customers to select a color from (this chart is simple rectangles of color created in InDesign) and I need to coordinating colors coming from graphics to match it."
Your goal, at this point, is to establish what file types customers are going to bring you. Your workflow needs to be industry standard. It looks to me like you are attempting to create your own color space, which happens to match InDesign output on a print chart. If you are anticipating a strictly photographic color environment, color matching is not a priority. If you are attempting to output evrything in the desktop publishing world, then you need to setup two work spaces: one photographic, one graphic arts. Each environment has its own color characteristics and they are not the same.
"In my research online, I saw some people saying to use LAB colors??"
Not necessarily. Focus on getting your applications to work together, first.