Think about this. If your motor home significantly rocks side to side when people move around inside, it must surely sway much worse when being driven.
Consider investing in heavy duty front and rear anti-sway bars also called stabilizer bars, instead of stabilizer jacks. If your results are like ours, you won't need jacks for what little motion remains when parked. You will also benefit with the handling while driving. The rig will be so much easier to keep in a straight line, and will have much greater control on mountain & canyon roads. So safe and comfortable for your passengers too.
Hellwig makes nice heavy duty sway bars at a reasonable purchase price, and many people install them by themselves. There are a number of do-it-yourself youtube videos. I especially like the Tito series
HERE.
And yes, check those shocks too.