The best exercise for strengthening the back is the Bird Dog Exercise
(kneeling two point stance) and any type of rowing whether with dumbbells, bands, cable machines, or suspension trainer.
Pelvic stability is definitely a component of a strong back but it's the postural muscles that need strengthening for long periods of sitting and the bird dog is the most effective and least dangerous.
A great laying exercise for a strong back would be the Prone Cobra
. It takes about 2 weeks of doing this 2-3 times a week to see a major difference with my 60-80 year old clients who have virtually no back strength and the great thing is you don't even have to raise as high as the girl in the video. It's probably the most effective postural exercise ever