She had somehow managed to push hard enough on one spindle to break it at a narrow point, leaving the lower half pointing dangerously upwards, and the top half was half way across the bedroom.
Lacking a lathe (note to wife...), I headed for the next best thing: the drill press. I happen to have some 1/4" dowel stock on hand, so I drilled a one inch deep hole in the centre of the top and bottom halves of the spindle (make sure they are centred and matched!), and then I cut a 1-3/4" section of dowel and dry-fit the pieces.
With the pieces ready, I headed back to the bedroom with the spindles, dowel, glue bottle, a damp rag, and a 3-foot clamp. For the model of crib that I have, the top and bottom of the spindles are very slightly tapered. This means that I have some wiggle-room when it comes to spindle height. So I put the top half of the spindle in place and pulled upwards with the top of the crib against my chest, to force the spindle as high as possible. Then I placed the lower half of the spindle in place, put some glue in the dowel hole and along the exposed shoulder, and inserted the dowel. I then removed the top half of the spindle again, added some glue to the dowel hole and again to the shoulder. The next manoeuvre had to be done all in one attempt, or glue would end up dribbling everywhere; I put the top half into its proper hole, pulled it as high as it would go again, pushed the lower spindle as low as it would go, lined up the dowel with the top half of the spindle, then straightened the spindle until the dowel slid into the hole. Make sure you have the top and bottom halves properly aligned so that the "teeth" match, or you will ruin the fit of the two pieces.
If you don't have a drill press, another option is to cut a notch in both top and bottom halves, and insert a small hardwood or hardboard spline. Do not simply glue the two pieces together without any support because it would result in an end grain-to-end grain joint, which is the worst joint for strength, and even a 15 month-old can break that joint!
Hopefully this helps you fix your next broken crib!