OK sounds like your back problem is pretty close to the one I've just recovered from.
First a disclaimer. I am not a physio so if you do the following and knacker yourself its not my fault.
I've found a few yoga positions and stretches that help which have been recommended to me by my GP and one of the trainers in the gym I go to.
Look up "Pose of a cat" and "Pose of a cow" and combine these two yoga stretches. Its basically on your hands and knees then arching your back upwards then arching it bach the other way towards the floor.
Next look up "Cobra pose" and "Pose of a child". Then start in the cobra pose and slowly move into pose of a child. I found pose of a child was really good for gently stretching out the affected muscles in my lower back.
Next lie on your back and grasping your knees pull each leg into your body. First one at a time then both together. This is good for releasing your glutes and lower back.
Next work on your hamstrings. Sitting on the floor with legs apart and toes facing the ceiling try to touch the toes on one foot then the other.
Then standing up stretch upwards to the ceiling as far as you can then slowly bend down to touch your toes or as for towards them as you can. Then stretch up to the ceiling again and arch you back backwards as much as you can then stand stright and relax.
I'm also working more on core strength now I'm back in the gym as I don't want this develop into a weakness that's going to give me recurring back problems.