Can I reuse a /2 cable for a 120V subpanel? (formerly an old sub wired 2-pole 30A for my trailer)
Yeah, that's fine, but you'll have to rearrange things a bit to make it work.  

However, you'll need a disconnect switch

The best way to get that is to fit one more breaker, and backfeed it.  (i.e. the supply comes in where the power normally goes out).  

A backfeed breaker requires a tie-down kit to be applied.   Tie-down kits only fit on 2-pole breakers.  (it's called "pole" by the way).  

Normally, you would split the feed, e.g. with a wire nut and 2 pigtails, to this 2-pole "master" breaker.  

I'm not sure why you're getting such a small panel (in terms of spaces).  But since you are out of spaces, we can do a trick.    On the 2-pole breaker, one side is the backfeed side from supply.  The other side is one of your 30A loads that you mentioned. So this breaker is serving as both the disconnect switch and a branch circuit load.  Not elegant, but it will work.  

"But wait. I am only backfeeding one leg.  How does power get to the other leg?" 

Surely this panel has main lugs. You run a wire from one main lug to the other.  I recommend a #3 Cu wire since it is a 100A panel after all. But a #10 would be safe for now.  

Okay, okay, I hear you on "big panel". How do I wire that?

If the new panel has a main breaker, use that for the disconnect switch. Simply put two #10 pigtails on the two "hot" terminals and wire-nut them to your #10 wire coming in. (use a big tan or red wirenut). 

If your panel is "main lug", you still need a disconnect switch, so you'll be forced to backfeed a 2-pole breaker again. Since you have the space, go ahead and get a 2-pole breaker with tiedown kit, and do the "two #10 pigtails" thing as described in the last paragraph.  (we didn't do that with the 6-space panel because there wasn't room). 

Then proceed normally.

Remember do not put MWBC (shared neutral) circuits in a 120V panel.