I have read that if you have 10BTC you would also have 10BTU??
Im confused about how this would affect the difficulty?
Would I be mining BTC or BTU?
Yep, however much BTC you have you would have an equal amount of BTU. The difficulty will be affected based on how many people are mining each chain and we can't predict this outcome (or what exactly the price would be of each strain or whether it's profitable).
Do i choose? Does the pool choose?
You choose, but the pool is deciding whether to support the hard fork - so if you're mining in a pool that supports it, your miner will be contributing to it happening and it is likely that the pool would be a pool for BTU in the future (you could always join a BTC pool).
Stores that currently accept bitcoin - would they still take bitcoin? Would they take bitcoin unlimited? Are they the same? Does one supersede the other? Is it just like an additional coin like an altcoin?
Stores that accept Bitcoin would take whatever they choose. I doubt that any small merchants would take BTU and I think most will stick with BTC, but that's just my opinion.
They aren't the same but they are based on the same thing to put it lightly, so BTU would kind of be a development of BTC which supports bigger blocks/miners choosing to change the block size at will (which I disagree with). Some people say it's an altcoin as it is a separate coin from BTC which is mined separately, but it isn't, of course, the same as an altcoin as it has to be supported by a large amount (over half and most likely over 75%) of the hash rate (computing power for mining).
I hope that was clear enough. Don't worry though, it might not happen at all.