Can I run two sets of 10/3 30amp wire to feed one panel?
That's a violation two ways.
First, you can't parallel.  Paralleling requires special equipment rated for paralleling on the supply end - this is for a bunch of reasons.   It is also not allowed below a fairly large wire size.  It's also uneconomical below an even larger wire size, and as a result, nobody makes paralleling equipment except for really huge wire.   NEC 310.10.
Second, you can only have one supply feed to a building.  NEC 225.30.
Bonus violation: Can't use NM cable outdoors, not even in conduit.  (especially not in smallish conduit!)
Anyway, it sounds like this is about economics.
Here's a fact nobody knows: 10/3 UF and 2-2-2-4 MH feeder are about the same price, even though one is 30A and the other is 90A.
Use 2-2-2-4 MH feeder.  Save the valuable 10/3 for something that actually needs 10/3, like ... .... a dryer, or range/oven separates, or shrug TWO travel trailers?  Sell it on Craigslist?
60A breakers are 1/3 the price of 90A breakers, so go ahead and breaker it at 60A if you want to pinch pennies there.  If you ever develop the need for 90A, you can change the breaker to that, then. Use the cost savings on a nicer subpanel, because &quot;number of breaker spaces&quot; is one place never to scrimp!  A 24-space is not excessive, and nice thing, the combo packs come with a bunch of breakers!
You'll need a subpanel anyway, since you can't put #2 wire directly on a receptacle, and a subpanel is the cheapest possible way to get 4 lugs to adapt #2 down to smaller wires.
MH feeder is aluminum, but that's perfectly fine for large feeders like that.  (which is funny because you never expected to use a large feeder, eh? :)