Hi J.,
I would take dressy-casual to mean the same as business-casual: slacks or chinos with a dressy or button-down casual top, or a nice knee-length or ankle-length skirt or dress. No cleavage (front or back).
For men/boys, a simple button-down or polo/golf shirt tucked in with a belt. (and no baggy-butts for the boys!)
No gowns; no silk fru-fru; no ties or jackets. No sneakers or pumps, but loafers, sandals, flats, clogs, and leather lace-ups are probably all okay. No athletic socks.
It is not right of your previous hosts not to acknowledge your cash gifts. That's just bad manners. It shouldn't matter what you give, as long as it is from the heart (and includes a gift receipt - lol!). The bride and groom's parents should remind them how important a simple "thank you" card can be.
Have fun!
t