I don't see a real point in doing a lot of ground work if things are going ok in the saddle.
I disagree with that personally. I see so many horses who have shocking manners on the ground, because people have only concentrated on ridden training.
I teach 'lunging' as just a progression of leading or driving, at gradually increasing distance. So I'd teach a horse to back or turn first with direct(fingertip, etc) pressure on the bit I want to yield. Eg. Nose or chest for back, flank for turning HQ away. I then teach the horse to yield with indirect pressure - eg. Pointing my finger, stick, swinging a rope, etc. I use direct pressure to 'back up' my requests if they're ignored or not understood.
Once the horse is good at yielding to indirect pressure in all ways, then it's just a matter of 'testing' it out at bigger distances & calling it 'lunging' when the horse is at a certain distance & doing it in circles!
Sidepassing is taught in the same way. It's generally easier for the horse to understand yielding forehand & HQ separately, so when they're good at that, I alternate steps of fore & hind yields until the horse is alternating so quickly as to go sideways. Once I get sideways, then I 'refine' the cue until it's one cue around their belly, rather than near their shoulder & flank/hip. This is also where your leg will be for ridden sidepasses. Once you've got the behaviour, then you can gradually improve specifics, such as stepping the feet across correctly. It's also helpful to start with a fence in front, to block forwards as an option.
Don't discount the possibility of physical problems with regard to backing up - perhaps hock or sacro probs mean the horse is actually unable to walk backwards easily.