After removing the top, I drew in ¼” x 3” rectangles where I planned to add hardwood splines, at all 4 corners of the table.
First, I drilled ¼” x 2” deep starter holes at one end of the rectangles. Then I used my router, with a ¼” upcutting bit, to rout in several passes ¼” wide by 2” deep grooves along the length of the rectangles. Next, I glued and tapped in ¼” x 3” long x 2” deep hardwood splines.
The final result was a rock solid table, finally with strong joints.
This sketch shows the concept; looking down at the 2x2 leg and the 1x4 aprons that support the top. In dark is the added spline.
Step 1: Mark out location for reinforcement
Step 2: Cut the groove
Step 3: Groove completed
The grooves were about 2" deep.
Step 4: Glue and tap in the spline
The grain on the spline should be legthwise, that is, from left to right in the photo.
Step 5: Completed spline
Looks kinda ugly here, but it is really strong!