Hiya,
One thing to remember that Ireland only came into exsitance about 80 years go. Until then anyone born in what is now Ireland was a British Subject. However, Britain does not allow cirtizenship to be passed through grandparents, only through parents. There is an anecstry visa for those who have british granparents and are commonwealth citizens, but as the US is not in the commonwealth that dosen't apply to you so you better stick with the Irish route.
Also, Belfast is not part of England or Britain, its is however, part of the United Kingdom of Britain and Northern Ireland.
In terms of your EU working rights. Its important to remember there is not such thing as an EU work permit. Each country issues its own paper work. The treaty of Rome (1957) requires EU members to allow free movement of labour. In practice this means an EU state cannot impose any requirements on EU nationals to reside/study/work that it does not impose on its own nationals. Remember that some EU contries are more berocractic then others. So a German could just enter the UK and go apply for a job with their German passport or identity card. If, however, a Brit wanted to move to germany they would have to first go to the local beurocracy in Germany and get their papers sorted out. Its a fairly simple procedure and Germany is obliged to issue a Brit papers under EU treaty, but the Brit has to jump through more hoops simply because a native german would have to have these same papers to work in germany while a British person dosen't need any paperwork except their passport to work in Britain.
In terms on non-European spouses of European nationals exersising their treaty rights in third countries. That is if you and your husband choose to move to the UK for example you would be the non-EU spouse. You would need an EEA family permit from the British embassy. If you choose to move to France you would need an EEA family permit from the French Embassy. You can only use get your EEA family permit for the country your EU national spouse is moving to and it is only valid in that country. THat is you cannot move to France and leave your husband in the UK.
You might be able to do the EEA permit in country, but it might depend on the particular EU contry. Most of the time when entering the UK for example you are assumed to be a tourist. You might be asked how long you plan to stay and if you say you plan to live there and you have no visa they won't be pleased.
I would suggest you contact the embassy of the particular EU country where you plan to live and ask them about what requirements they have to issue an EEA family permit.
Marka