I think you need to find a really good yoga teacher who could help you. I would recommend an Ashtanga yoga teacher because that it is one of the most traditional styles. The Ashtanga primary sequence is about moving through the postures in a sequence which builds heat in the body. This heat increases your flexibility. (This isn't any "mystical heat" like Tummo. It's the regular heat which comes from hard exercise, i.e. sweating your a** off.)
If you do these stretches cold without any warm up. It's no wonder you get little results. The Ashtanga primary series begins with many repetitions of Sun Salutations. The primary series could also help your back.
As for the streching poses I do, I don't do any special breathing. I usually keep the body in each position from a half to a couple of minutes.
Breath is the fuel for your body. Using special breathing can help you get more out of your body. In Ashtanga, the ujayii breath is used. This is basically deep breathing through the nose which makes a "whooshing" sound in the back of the throat (think of Darth Vader doing yoga on a Star Destroyer). In Ashtanga, you inhale deeply and then go deeper into the stretch with each exhalation. When you can't go deeper, you just hold it and breath deeply there for a while.
Why do have reduced mobility in one side of your body? Is it neurological (from a stroke, etc.)? Or is it physical (from an old sports injury, etc.)? If it's physical, you might want to look into deep tissue massage. You could perform it on yourself to break up adhesions in the connective tissue which may have resulted from your old injuries. If this is the case, these adhesions are stopping you and not your muscles.
After about 2:30 in this video this man who is a martial artist and a chiropractor talks about this.http://www.youtube.com/user/howtostretc ... p00_XHvhgI
Another thing you could try is isometric stetching. This depends on a very handy reflex of the body. Basically, you contract the muscles being stretched by opposing the motion of the stretch and hold the contraction for five seconds. Then you go a bit deeper into the stretch and repeat. When you can't go any deeper, you hold the contraction for 30 seconds (this can be very intense!).
For example, if you're doing a split. You would try to squeeze the ground with your legs by contracting your inner thigh muscles and then you'd try to go deeper into the stretch.
You have to be in good condition to do isometric stretches, though, so you have to be careful. Maybe just use isometric methods with one or two stretches that give you the most trouble.