If only 10% of miners are mining on "Blockchain B" then they will still have the same difficulty resulting in each block being found on average every 100 minutes for about 2 weeks.
Who will still be using a blockchain where the block discovery slows by 10X?
Bitcoin's difficulty changes after a certain amount of blocks found (2016 blocks), not after a certain amount of time passed. It just happens to normally take about 2 weeks. It would take much, much longer if blocks were 100 minutes apart.
I imagine merged mining would be possible if there were 2 coexisting forks of Bitcoin (but I'm not certain of that). In that case, both chains could be mined by 100% of the existing miners.
The only thing that determines whether or not a coin (or fork) continues to exist is supply and demand.
I believe that a modest tweak needs to be made in order to allow merge mining. Just a bit of space per block iirc. I think it would be a good addition for anyone who is going to do a hard-fork (which I believe might be necessary, but I could be wrong about that.)
Actually, I'd be really interested to see a different proof-of-work scheme upon hard fork. A random (or weighted) selection of CPU-friendly algorithms do solve blocks seem to me that they would result in two worthwhile goals: 1) making it feasible for independent nodes to mine again which would produce incentive for broad node distribution, and 2) precluding attack from the build-up of sha256 asic farms. The current mega-miners obviously would not like it, but what are they going to do other than to try their level best to make a pure sha256 fork be dominant and use whatever money/power they can muster to attack the fork in standard ways available to most everyone?
My interest in Bitcoin has been as a backing store (a-la sidechains) from pretty much when I got started back in 2011. My rational for wanting Bitcoin to be as ultra-lightweight as possible is that I would see everyone who is running sidechains of any type as also running Bitcoin nodes. That is how I would see the infrastructure supporting the solution be broadly distributed. If sidechains compete among themselves for settlement on the backing store, and need the backing store to be rock solid, they have several incentives to support it irrespective of the payout for doing so. Running Bitcoin infrastructure at a profit or at least a break-even would be great and likely quite possible.
I'm lobbying for the Blockstream guys to take the opportunity offered by Hearn and Andresen to do some major hard-fork changes of their own. Possibly along he lines of what I mentioned, or other. If I have to choose a fork anyway, I'm anxious to choose one which I think has long-term potential. I see the best outcome for humanity coming out of a total war, and Hearn+Andresen drew first blood. Alternately, I'm fine to see a split be amicable and each fork can stand on it's own merits. I'd still want to see a highly defensive posture and MAD-inspired strategies ready to be called into action if necessary.