Go wireless? Just about everything is wireless these days. :C
I've usually gone with 1" PVC for underground when 1/2" or 3/4" would work. Small cost difference from 3/4". Makes pulling longer distances easier and allows for future pulling in of more or larger wire. You'll want max. 4 x 90 degree bends overall. Poly water pipe can be used providing you use the correct wire/cable.
Another option would be aluminum mobile home feeder cable. Min. size is #2 (4 conductor) and good for 100 amps. The stuff is cheap, like a dollar a foot and faster to install. I'd go with above suggestion and install a small sub-panel in the garage and a circuit for the RV outlet. That will give you a breaker you can shut off when plugging in. Can use a smaller breaker in the house panel like maybe 60 amps or larger up to 100. Would give more available power for other stuff/tools/equipment/heater in the garage. You could also use a junction box to reduce the wire size to something smaller if wanted.
I've used armored teck cable for direct burial a few times but is expensive unless you can find a smoking deal on it somewhere. Perhaps you could check CL to see what cable might be for sale.
But why not use the existing 1" conduit which is good for 3 x #3 (code burial depth requirement notwithstanding), pull in larger wire and install a sub-panel.
On voltage drop, start with the actual voltage at your house panel, not a nominal 120 volts unless you know it stays at or close to 120. Could be lower during the summer heat or other peak periods. Use a voltmeter and leave it there for 24 hours and see what it's like. But do you really need a full 30 amps available for your RV?
Instead of a ditch witch I'd go with a mini excavator from a rental shop. Or just dig it by hand depending on soil condition. Check the Code for min. burial depth, backfill material & protection.
