Joint Tenants always own an identical and equal portion of the property and equal rights to the entire property – if there are two tenants, they each own 50%, if there are four, they each own 25%. Tenants in Common can specify ownership interests. Can you cite some authority that states otherwise? I don't mind being corrected if the correction is actually true.
It would be hard to argue that flipping a single house constitutes being in the renovation business.
The IRS' position is that you should allocate gains according to ownership interests unless you are in a community property state. Otherwise, I could be in a very high tax bracket and push a capital gain to my wife's separate return and have it taxed at the zero percentage rate. That is not allowed. It is no different for a house than it is for a joint stock brokerage account.

