William, there are several different kinds of stain and different things will remove them. The normal process is to take a sample piece, strip it, apply household bleach and see if that has any effect. If it does not, mix up some oxalic acid (Sold under the name Wood Bleach) and try that.
But remember that mahogany is pretty dark wood and you can not easily lighten it much from it's original color. Also, when you apply a finish, it will darken. You get the same effect by putting water on the wood. The wet color of the wood will be the color after a clear finish is applied.
I don't quite understand where you are trying to go with the wood. I would not paint wood that is a pretty as yours, but it is your house. There are ways to do the decorating that should allow it to be used to it's and your best advantage. Let me know if I can answer any more questions. Remember to wear gloves and eye protection when you are using chemicals and wear a dust mask while you are mixing the oxalic acid.