Hi,
I don't know why would u try to get another EU country residence card once you have one for UK ? anyway here are the info:
Your brit spouse must be residing in Ireland and exercising her treaty right here . exercising her treaty rights means that she must be involved in any social activity like, work, study, or she must be financialy sound to support herself and you.
Once she could prove that, than you have to go to the irish embassy to get an entry clearence, if every thing go smooth you would get a visa for 3 months or six months. Once you arrive into ireland than you have to go to local garda immigration office to register yourself and apply for 5 years residence card on form EU1. which you could find more details here:
http://www.inis.gov.ie/en/INIS/Pages/EU ... y%20Rights
Hope i answered your question.