How the old miners will check the doublespending if money was spend earlier with new transaction type?
It is not a new transaction type-- transactions could always have multiple TxOuts.
However, to prevent a denial-of-service attack (which was actually attempted-- see block 71036) transactions with more than 2 TxOuts are currently dropped by clients instead of relayed.
Now that there is a need for it, the rules allow "reasonable" multi-output transactions, but still denies "unreasonable" ones (reasonable means: is one of the 2 standard transaction types and only does one ECDSA signature verification per recipient).
So: no, this won't cause a block chain split. And no, old miners will not disagree with new miners, so double-spending is not possible.