Have to agree with Bulli.
Pressure should be 26/28 front, 36/38 rear
What size tyres are they and what size rims?
Perhaps the rims are too narrow for the tyre, which is pinching the beads?
This will cause the tyre to bellow out and slip sideways within the tread width.
I'd be more inclined to think your springs are shot.
If they're weak, they'll give-way under certain driving conditions.
How old is the motor? If it's the '90 Disco, then no rear anti-roll bar will affect the handling.
If it's the '98 Disco, perhaps the suspension is a little saggy from the LPG tanks weight?
I'd certainly consider changing the bushes on the vehicle as a matter of course too.