From what I've read on this .... (just went through treating driftwood) ... you boil it no matter what. This will kill fungus and bacteria and such, as well helps release the tannis contained in the wood. And to release the tannis from large chunks, soak it in tubs of water (weighted down if needed ... so all is submerged). As the water will change colour (tannis releasing) you'll need to replace the water. Keep doing this until water stays pretty much clear (depending on size process could take a week or two, if not more). Once this is complete then you can wash the Large Chunks in boiling water to kill said fungus, etc. The tannis will change the colour of your tank water, and some may even remain after all this for a bit. Carbon filters are supposed to help clear up any remaining discolouration, although I lucked out and didn't have any remaining.
As for your backyard branches, not really sure. All I know is when I was looking into this, I was strongly advised by numerous people to use only hardwood and that the roots were the best.