How do I keep dyed leather panels from bleeding into each other when stitching?

The bleed is happening because dye wicks into raw leather edges through capillary action, expecially when it's applied heavy like you did on the head. Heavy coats sit in the leather and any moisture transfer while handling or stitching pushes it sideways into the neighboring panel. Two things fix this: lighter dye application in the first place, and sealing the joint line before the two colors ever touch.

What's worked for me on multi-color projects is to dye each panel, let it dry a full day, then seal just the edge that will meet the contrasting color before assembly. I've used a thin coat of resolene or even plain beeswax rubbed on the edge line, then burnished. The wax especially acts as a barrier so the green can't crawl into the yellow. You can also mask the adjacent panel with a strip of painter's tape right up against the seam while you're doing touch-up work later. Leather dye will find any unsealed path, so think of it like waterproofing a joint. On the order of operations, most people who do a lot of colorwork stitch first and dye last, or at least do the final dye pass after assembly. With a shaped bag like yours that's tricky because the seam line isn't straight, but you can still get a small brush in there and clean up the seam after stitching. Honestly, that might be your best move now: stop trying to prevent more bleed, finish the stitching, then go back with a fine brush and touch up the smudged areas. A light sand with fine grit paper on the smudge first, re-dye just that spot, and it'll look intentional. Edge paint over a finished seam is doable this late, yes. You'd apply it in thin coats with an edge tool or even a folded piece of card, letting each coat dry before the next. The catch is that edge paint is basicly plastic, so it will look slightly diferent from burnished dyed leather. On a kids' bag that's fine, and it's actually more durable for daily abuse. Do a test dab somewhere hidden like under the strap first to check the color match. If the seam looks decent after touch-up dye and a good burnish, you might not need the paint at all.

I'm not buying the 'just stitch it and touch up after' part. On a straight seam maybe, but that bill is a tight little curve and you'll be fighting to get a brush in there without hitting the green. Worse, yellow is one of those colors that never fully covers a dark smudge. I tried patching a black bleed onto a tan panel once and no amount of re-dyeing hid it, it just became a dull grey blotch. If I were you I'd stop stitching right now, let everything dry hard for a day, seal the remaining seam lines, then finish. Way less to fix afterward.

Watch your thread too. Waxed linen picks up dye off your fingers and the panel edges as you stitch, and it'll drag dark smears right across a light piece. Ruined a two-tone holster belt that way years back, took me three seams before I figured out what was happening. I keep a rag with a little oxalic acid on the bench now and wipe my hands and the thread every few passes. For the next one, consider doing what the old saddle shops did - assemble everything in natural leather, then color it after. Paint the details on top instead of fighting bleed between panels. Takes a steadier hand but there's nothing to creep.

One thing I'd add: build the bill as a seperate little pocket piece rather than a flat panel butted to the head. My daughter's owl rucksack had the same problem spot, and hiding the color transition inside a folded edge instead of a raw-butted seam killed the bleed entirely, since there's no exposed edge for the dye to wick along. That bag took me about 14 hours of stitching total and the seams are still clean two years later. On this one, if the smudge bugs you, a dab of matching edge paint on the yellow side of the seam line only will read as intentional on a duck anyway, they've got all sorts of odd color patches on thier faces in real life.