Now you've gone off the edge...
Excellent. Now attach a cross-brace 2x4 to the inside ends of those 2x4's, inside the bucket, to connect the "teeth" together & help them resist moving side-to-side (rotating around your clamp).
Oh, and cut the ends of the "teeth" so they're points! :thumbsup:
I think Jake98 is just jealous he didn't think of doing that. :laughing:
If you moved them out to the ends of the bucket so they are against the sides then put a cross brace at the rear they would be pretty well locked into position. You could also add a third fork in the middle for smaller branches.