Can I configure a two-stage thermostat to manage two heat systems?
I have almost the exact same setup as you (hydronic floor heat and air handler for backup heat) and mine works with one tstat just fine.  So while you aren't asking for too much from &quot;a&quot; thermostat, you may be asking too much from &quot;that&quot; thermostat.  I looked at the specs and didn't see anything about 2nd stage heat or aux heat, it might be there but I couldn't find it. On my tstat it's call &quot;aux heat&quot;. I think 2nd stage heat is for a 2 stage furnace or heat pump. When the more economical first stage can't keep up or you've turned up the heat a lot, the 2nd stage kicks in on the same device.
I think Aux Heat means a different heating device.   Ed Beal could probably contribute more here.
Anyway, I run a Honeywell RTH8500D.   And it does the job you want. I didn't hook it up, so can't give you the specifics on that. But what you want can be done and this is the tstat that works for me.