I have an extenda-stay and an extenda-flow installed in my propane supply line. I don't believe either are "quick connects". For reference, the extenda-stay allows you to connect an additional propane tank, & the extenda-flow allows you to connect additional devices (heaters, grills) to your motor home propane supply.
The extenda-flow can be seen at
http://www.pplmotorhomes.com/parts/lp-gas/50290.htm
I bought my kit (with both "extenda's") from Camping World. I have tried each to confirm operation, though haven't yet had to depend on either.
The extenda-flow that you asked about typically comes with a 12' hose. I bought a 5' extension so that I can easily place my grill on a curbside picnic table, while connected to roadside tank.
I met an RVer this summer who used airhose with quick connects like used in garages for air power tools. I asked him if it was safe (because I had no idea) and he said "absolutely,,, why not?"
So, it sounds like you just need to decide what fittings you need to accomplish the task. In addition to Camping World, I found a wide variety of fittings at TSC (Tractor Supply Co). You will be able to use your Weber, fueled by your motor home propane.