Lannie, there are things that you could do for the inside cedar, like bleaching, but I think that this would be a nasty, messy job and not turn out to be successful. With the rough cedar, sanding the stain away would also be a big mess and probably not all that successful either. Solid stains with Zinsser's B-I-N under it is one possible answer.
I think that I would start with the pro's near you, both at the independent retail store level and the actual painting/staining level. Hit a few places like your Sherwin-Williams or Benj. Moore paint dealers and ask for their thoughts and who is the best in the area for this type of problem. If you have it, probably others have too. The stores have a vested interest in ensuring that you get a good result and it can be a heck of a lot easier to get a real understanding from 5 minutes of looking at a problem than just seeing typed words. Real colors, shines, lighting, etc. is one place where seeing it is worth one million words.
After getting some ideas, go buy a cedar board, whatever stain that you think is on there now and some of the stains and sealers it is suggested that you use. Get your sample board or boards as close to what you have now as you can and then try the techniques that have been suggested. Then put them out in the room and live with them for a couple of days. One or 2 choices will immediately become apparent. and you can go from there, either on a D-I-Y basis or letting the pro do it. If you do it, and a pro or 2 has spent some time helping you pick a path, pay him/them extra for his time and effort. Who knows what else you may want to do in the future and word gets around about people who treat pro's right and those that don't.
On your outside cedar, yes you can remove paint from cedar with a power washer. You can also remove a lot of cedar! Practice, practice, practice or call a pro. No, calling a pro is not my answer for everything. You have to pick your spots. There are some jobs where starting with the art/skill level, and the experience, that a pro should have will save you a lot of money in the long run. Many jobs are homeowner friendly and many are not. And you have to be able to look realistically at yourown skill and experience level to make the determinations as to which is which. Enthusiasm, particularly enthusiasm only for saving money, is just not a good basis for doing some jobs.