Sealing it might keep the mold out in the future, but if you're going to have it as regular in-a-room-of-your-house full-time furniture it really shouldn't get moldy again unless you live in a swamp.
If you're going to sand and paint the whole side anyway, i.e. not try to rescue the black paint under the decals, I'd try something with acetone in it. Fingernail polish remover, paint thinner, something along those lines. A heat gun and a scraper might do the trick too.
Good luck!