And the IRS's Response: When you gave them your private key, did you remember to pay your gift tax?
I didn't give them "my" private key. It was never my property to begin with! The bitcoins associated with this private key were mined communally in a mining pool. Guess who the miners were?
Then all you're describing is a partnership. Your income is 1/# of miners, unless you have some agreement saying you get more or less than that, and you'll get taxed on this. Take money out, and you have taxable income. Leave the money in there, and the partnership is subject to taxation. Either way then, you still owe taxes.
And lack of documentation has never been a great defense to play with the IRS. You'll piss them off, but that's about it.