What if a pair of double-spent transactions are collected into a new block?
When Alice sends the bitcoin, she spends an Unspent Transaction Output (UTXO) created by a previous transaction. To create a doublespend, she has to use the same UTXO as an input for another transaction.

As every full node keeps track of all existing UTXO, it is trivial for all nodes to recognize these transactions as doublespend. A block containing two conflicting transactions would be invalid, and thus would not be accepted by any nodes.