I've had lower back problems for some years, too much sculling with flexed lumbar spine (rather than hip hinge) and not enough stabilising exercises. I did lots of Pilates but with no improvement in spine stability and was still prone to sudden buckling (whilst standing on one leg in the shower to wash the other, or rowing in an eight) and another frustrating week or two off from life, then working back.
I think I was pointed from somewhere here to Stuart McGill, who advocates spine stability and shoulder / hip joint mobility (PhD in spinal research at a Canadian uni - he seems to have done much work with weightlifters). Search for his book 'Back Mechanic' - scanned pdf available online. His 'Big 3' exercises are making a huge difference to my back stability and confidence; 3 exercises to do daily with care and precision.
I also know I have weak glutes and so am working on those too (glute bridges, prone sole to ceiling raises, split squats, hip drops, side walking with ankles banded, arabesques, banded clams...).