Assuming you had the funds for both transactions, it is likely the network would authenticate both. If you did not, the network would likely authenticate the first transaction and not confirm the second. Lack of confirmation means that those funds would not be debited from your BTC account.
That said, do what you need to in order to secure your wallet. Having the same wallet in two different places is generally not a good idea.
Thanks for the information.
Yes, both would transactions would have the full amount so I wonder which one overides which one ?