Most kids suspension bikes are piles of cat poo, whether full or front only.
It's better that they develop their skills on a rigid bike, because they do it at a speed they are capable of handling. If they have cheap suspension it's like riding a pogo stick - no damping. But, it encourages them to go faster than their skill level allows, so they then crash harder.
2-3inch drops and a few bumps should be within their capabilities - if not, then they should practice until they can deal with them. Some of our youngest kids have just done the regional school mtb champs and even the newbies coped with similar surfaces.
If they're nervous at 2-3 inch "drops", get them to go over them a few times until they're confident at doing it, then gradually increase the difficulty. Usual rules apply: stand up, keep knees and arms bent, weight back and let bike ride underneath them while their bodies/heads stay level.
Set up some artificial obstacles in a safe area (plank on brick, plank on two bricks, plank onto pallet and ride off - or even ride off kerb
There's also the fact that a bike designed with rigid forks may not be suitably proportioned if you install a suspension fork.
Once they can handle these and more severe obstacles and they're big enough for a better bike, they'll have the skill levels to handle the greater speeds that suspension allows.
On no account get a full susser!