How do you know the relay that controls your step does not work? Did you figure it out, or did someone else. On my MH, the BCC under the hood does supply power to the steps. It is powered through the (replaceable chassis disconnect relay) but the ignition override is powered through a small (ignition) relay built into the circuit board (not replaceable). But that same relay also powers backup camera, jacks down alarm, and TV cutoff.
If what you say is true, then run a new relay and wire that is powered when the key turns on. The steps are looking for a 12 volts to the yellow wire when the key turns on to make sure the steps retract (if the door is closed).
Here is a manual, look on page 7 for troubleshooting.
06 Hurricane 34FT WH W20 Chassis 8.1L 132K, Steersafe, Koni Shocks, DIY Trac Bar, Tri-Metric 2025RV Battery Monitor, 4-6V Batteries, Scan Gauge 2, Crossfires, 735W Solar Morningstar MPPT-60, WG T4 In-Motion Sat, XM Radio, 07 Chevy Malibu Maxx Toad, Falcon 2, Brake Buddy, Escapee