Since you don't need the 555 high current output stage, I'd use one CD4093 quad Schmitt NAND gate to do both the main output pulse and the inhibit timer. The leading edge of a positive-going input pulse triggers the main output, a positive-going output pulse. The trailing edge of the output pulse drives a second R-C timer that inhibits the main input through a NAND gate. With two R-C networks, the output pulse width and the inhibit time are completely independent. And, fewer parts than two 555's.
Whipping out a schematic is a bit cumbersome these days, but I'll try to post one tomorrow.
ak