What I was emphasizing on is that both the old transaction and new transaction can be included in a block since a miner can pick just any transaction (although they use high fee as the priority) they want from there mempool to include in a block they miner.
This cannot happen, if the mempool node is not full RBF enabled. Any transaction that does not contain the RBF flag will not be accepted. However, if it is full RBF enabled, the old transaction will be removed, and what you say can only happen in two different nodes, so that when you broadcast your transaction to a node Your old transaction in a different mempool will have been confirmed, as the miner has mined the block and included your transaction, and here the new transaction will be invalid.
But if you mean Child-Pays-For-Parent transaction, it is different from RBF.