As an EU citizen, you're entitled to move to any EU country that you're NOT a citizen of and bring your spouse with you. As such you have the right to bring your spouse to Spain, but not Ireland.
The fact that you're working in Gibraltar is irrelevant. It's no different to moving to Drogheda and working in the North, except that as an Irish citizen in Ireland your spouse wouldn't benefit from treaty rights, like she would in an EU country like Spain where you're not a citizen.
In this situation, your spouse could live with you in Spain, but possibly not travel into Gibraltar, unless she can do so already as a tourist, with her existing citizenship.
As the spouse of a non-Spanish EU citizen, she would have the right to work in Spain, but I don't have any information about the rights of spouses of British citizens to work in Gibraltar without living there.