Fixing double-ball joint on a 6'' scale action figure
The latter idea of fixing the broken peg sounds the most practical. Strengthen the connection by inserting something strong, like part of a paper clip or a toothpick, to bridge the two pieces. If there is enough material there so that you can tap (drill) a small opening for the wire that is, just sticking something in without making room for it may split the plastic.
Also the choice of glue is important. There may be something stronger than super glue for the bond and some plastics may even take damage from it. Maybe the manufacturer sells or recommends one, or search on here for adhesive questions, there have been a few.