Can receiving money make a transaction fail?
No.

The addresses in Bitcoin only signify ownership. You don't need to spend all money from an address or any such thing. The atomic units of Bitcoin transactions are Unspent Transaction Outputs (UTXO).

UTXO are uniquely identified by the txid of the transaction that created them, and their position in said transation's output list. 

E.g. if the transaction id of transaction1 were tx01 the 49.99mBTC output to Alice would be tx01-00 and the 50mBTC output to Bob would be tx01-01 (computer scientists start counting at 0).

To spend a UTXO, you'd reference them by this identifier, i.e. "I want to spend tx01-00". Then you need to provide a signature that corresponds to the address that tx01-00 was assigned to, and you get to reassign the balance that tx01-00 represents. Afterwards, tx01-00 is invalidated.

So, in your example transaction1 spends UTXO that are unrelated to transaction2, so transaction2 has no bearing whatsoever on transaction1.