Miter each end of the 2-inch by 2-inch by 12-inch long and the 2-inch by 2-inch by 24-inch long pieces of stock wood to a 15-degree angle, using a table saw and miter fence. These are the support bars.
Clamp the two 60-inch long pieces together at each end, using C-clamps, with 2-inch cardboard squares padding the cups. Place the clamped pieces in the work rest of your drill press. Drill a 1/4-inch hole through both pieces, 2 inches from one end. Remove the clamps.
Lay the 2-inch by 2-inch by 12-inch piece support bar between the two pieces of 2-inch by 2-inch by 60-inch stock wood, 12 inches from the ends of the two long pieces.
Measure 24 inches from the front edge of the 12-inch wood piece along each of the 60-inch pieces. Center the 2-inch by 2-inch by 24-inch support bar between the two 60-inch pieces, adjusting position until the long pieces stay flush against each end.
Apply carpenter's glue to each end of both support bars, and to the last two inches of the inside faces of the long pieces, using a 2-inch wide paintbrush. Return all wood pieces to the correct positions and secure them with bar clamps. Tighten the clamps just enough to make the glue bead along the joints.
Wait 30 minutes and gently scrape away any excess glue. Buff any glue spots with a medium-grain sanding block to ensure that glue residue does not ruin the wood's finish later. Allow the glued assembly to cure overnight.
Drill 1/16-inch diameter holes through the handles and into each of the support bars 1-inch deep. Countersink all holes. Secure the handles to the support bars using 1/8-inch diameter, 3-inch long brass wood screws to create your wheelbarrow support frame.
Slip the axle of the child's front tricycle wheel assembly through one of the holes at the front end of the wheelbarrow support frame. Slip the wheel on and slide the end of the axle through the other hole in the support frame.
Slip the cotter pins, which look like large, odd-shaped hairpins, into the holes in the axle and spread the open ends until the pins do not move when jiggled.
Have a helper hold the two 12-inch by 36-inch by 1/2-inch pieces of plywood upright and 23.5 inches apart on their long sides.
Apply carpenter's glue along the 1/2-inch edges at each long end of the 12-inch by 24-inch by 1/2-inch plywood piece and the 4-inch by 24-inch by 1/2-inch plywood piece.
Press the 24-inch long pieces between the 36-inch long pieces, with all corners flush, to create the four sides of the wheelbarrow box.
Secure 36-inch long pieces to the 24-inch long pieces using bar clamps at the top and bottom of each end of the unfinished box. Apply just enough pressure to make the glue bead along the seams.
Wait 30 minutes before scraping away the excess glue and sanding any spots with a medium sanding block. Allow glue joints to dry overnight.
Apply glue along the 1/2-inch edges of the two 12-inch by 36-inch sides and the 12-inch by 24-inch side. Place the 24-inch by 36-inch by 1/2-inch plywood sheet on the box frame, making all corners flush. This creates the bottom of the wheelbarrow box. Clamp the bottom to the sides while the glue cures overnight.
Drill 1/16-inch diameter pilot holes every four inches along the bottom of the wheelbarrow box and into the sides. Countersink all holes. Secure the bottom permanently to the sides using 1/8-inch diameter, 3/4-inch long brass wood screws.
Repeat drilling 1/16-inch diameter pilot holes through the sides and into the 12-inch by 24-inch front piece, and again for the 4-inch by 24-inch rear piece. Countersink all holes. Secure with 1/8-inch diameter, 3/4-inch long brass wood screws.
Center the box on the wheelbarrow frame, with the tall end of the wheelbarrow facing front, flush with the front edge of the 12-inch support. Drill two 1/16-inch diameter holes 4 inches apart, through the bottom of the wheelbarrow box, 1-inch into each of the long pieces of the wheelbarrow frame. Secure with 1/8-inch diameter, 1.5-inch long brass wood screws.
Sand the handles, rounding the edges until they feel comfortable in your hands. Smooth the entire wheelbarrow, using coarse through extra-fine sandpaper. Apply five coats of clear acrylic wood sealant, allowing to dry 24 hours between coats.