Thanks, Steve, for the vinegar idea. I didn't have any scotch brite pads, so just carefully used the edge of my pocket knife. It didn't work before the vinegar soak, but it did, with some patience, after leaving a vinegar-soaked piece of paper towel over the glue and under a coffee cup for an hour.
As to the cabinet latches, they appear to be made by 2 companies, probably related in some way, since the design from both is identical. I found the half that breaks, the hook (aka "strike"), at various retailers online for prices that vary from $1.99 to nearly $10. Most are priced around $5+. Then tack on $6-$10 shipping. It's pretty ridiculous for a little piece of plastic that looks like 59 cents. The strike comes in two sizes or strengths, 5lb. and 10lb., but the 5lb. one is the one that breaks. The latch half doesn't break, at least not for me yet, and will accept either size strike.
Joel