Kevin, generally I would think that replacing it with an aluminum screen door would offer a longer term cost advantage but obviously you have a reason for the wood door. Here is something that you can try. Sounds like the screws in the closer pulled out a chunk of wood. (If the screws just pulled out, then put toothpicks in the hole and replace the screws.) To replace a large section of wood, get some Bondo from an auto repair store or Minwax Wood Filler from the home center. Both are basically the same products but the Minwax costs 2-3 times more than the Bondo. Mix according to directions and glop it into the cavity, with the door removed and lying flat, to a little more than full. Sand to level and paint to match. Drill pilot holes and replace the screws. Reinstall the door. Instruct the kids to go out another door.