I say not a problem. No need to have two hots.
Only issue would be trying to draw more than 30 amps total on the #10 feeder but you say you won't. Worst thing that could happen is tripping the 30 amp breaker back in the house main panel. Length of the #10 could be an issue for voltage drop if wanting to draw at/near 30 amps.
If this were installed under article 551 for RVs, the NEC does not require simultaneous demand loads of 30 and 20 amp recept. to be included in sizing wire to a pedestal and a pedestal "panel" doesn't require a main breaker in it.
If this were a remote garage structure on the property, a main breaker in it's sub-panel would not be required for less than breakers with less than "6 handles" total in the sub-panel .
I believe that you will require at least one ground rod, and maybe two by the latest code edition and of course, neutral and ground cannot be bonded together at the pedestal panel.
If you already have been using a 30 amp recept. only, then I would think that voltage drop hasn't been a problem but you might want to check the voltage at the pedestal just to make sure it's looking okay.
If still in doubt after reading all the posts here, google "mike holt" along with "remote sub-panel disconnect" or go to the Mike Holt electrical forum and ask there.
Good on you for knowing it's important to shut power off at a pedestal before plugging in you shore power cord. Reason is that a converter has a momentary inrush current due to it's capacitors which causes pitting on the plug blades and inside a receptacle which in turn attracts dirt and creates resistance and heat. Not necessary for plugging in anything that isn't an RV (tools, lawnmower, etc.