I would advise that you look at this link for information about spousal rights.
To be on the safe side, I would also advise you to contact the South African embassy about your situation, as there might be a required amount of time that you have to be married to your spouse for in order to apply for an EU passport.
Please let me know when you find out, in order to assist other expats who might have the same problem.
Yes you are correct, as it mentions on the work permits page, with an EU passport you do not need to apply for a work permit.
You are are right, your brother's dutch passport won't help you get residency/work permits for Ireland, so you'll have to figure out another way.
Start by reading our Work Permits for Ireland page.
To get a work permit for Ireland you'll need to have a job offer for a position which pays EUR 30,000 per year or more. Then the employer will need to apply for your permit through the Department of Jobs, Enterprise and Innovation.
What field of work are you guys in?