Extending 90 day visa

http://www.citizensinformation.ie/en/travel_and_recreation/travel_to_ireland/visas_for_tourists_visiting_ireland.html
"Even if you do not require a visa to enter Ireland, all non-EEA nationals, including those with visas, must obtain permission to enter the State by reporting to an Immigration Officer at the port of entry. The length of time you will be allowed to stay in Ireland is determined by the Immigration Officer but will never exceed a maximum of 90 days."
"The visiting/holiday visa issued to you allows you to enter the State once. If you have wish to leave for a short while and then return you must apply for a re-entry visa. (See 'How to apply' below for information on how to apply for a re-entry visa.)"

" What do I do after my arrival if I wish to stay in Ireland for longer than 3 months?
Visit/holiday visas are only granted for short term stays and never exceed 90 days. It is not possible to extend your stay beyond 90 days. You must leave the State on or before the date which has been stamped on your passport by the Immigration Officer when you entered."

So you might look into going to the continent and then come back...you'd have to check the details, but it might buy you another 90 days.
Good luck.

The above reply is correct with regard to the law. Actual practice is sometimes different. As a citizen of NZ and a spouse of an Irish citizen, you might well find a sympathetic Garda immigration officer willing to bend the rules in your case. I would attend your local Garda immigration officer, with your spouse, bringing your passports and marriage cert, and ask if they will give you an extended stamp. Do this some time before your current stamp expires. They may refuse, but then again they may not.

If you do have to leave, you only technically are required to leave the common travel area (basically Ireland + UK), not the whole EU. They say you're supposed to be gone for a full 90 days but in practice this is hardly ever enforced except with visa required nationals. The odds are you could go to Wales for a weekend, come back and get a new 90 day stamp. Many many people have been able to do this, though of course, you're not guaranteed to be one of them.

Finally, you could just overstay your permission. Ireland doesn't have exit controls, so you won't be recorded as an overstayer on your eventual departure. They're not going to hunt you down and even if your unlawful presence did come to their attention, they can't simply deport you - there's a rather lengthy procedure involved. Basically Irish immigration has more things to worry about than NZ citizen spouses of Irish nationals and unless you're going around robbing banks or something, they really are not likely to care that you've overstayed a bit.

As your spouse is an Irish citizen, his - and your - rights are governed by Irish law, not EU law when you are in Ireland.

So your question is "what rights do I have under Irish law". I think you were lucky to be allowed entry as a tourist as generally you have to go the spousal visa route even for a short stay.

In short, don't push your luck otherwise you could end up barred from Ireland - and have difficulty entering any other EU country.

Spousal visas are only required for spouses from a visa-required country. New Zealand is not such a country.

There is a significant error in #2: at the end of your 90 days you are required to leave the Common Travel Area (CTA), which is Ireland and the UK, so a weekend in Wales would not help -- you would need a weekend in France or somewhere.

Note that if you enter the UK as a tourist you are allowed 180 days (six months) in the CTA. Had you entered the UK first and then gone on to Ireland your stamp from the UK would have given you a six-month stay. If you now leave Ireland; have a weekend in France or anywhere outside the CTA and then enter the UK, if you are allowed in you will then be given six months that you may spend in Ireland.

There is no error in #2. If you actually read what I said, I told OP that she was technically required to leave the common travel area at the end of the 90 days. It is a fact that this requirement is not always enforced in practice, however.

If you do have to leave, you only technically are required to leave the common travel area (basically Ireland + UK), not the whole EU. They say you're supposed to be gone for a full 90 days but in practice this is hardly ever enforced except with visa required nationals. The odds are you could go to Wales for a weekend, come back and get a new 90 day stamp. Many many people have been able to do this, though of course, you're not guaranteed to be one of them.

A trip to Wales would not help: you would still be within the CTA and you might return to Ireland without passing Immigration and so would have no opportunity to collect another 90-day stamp.

Note that if you choose to overstay you would thereby invalidate your insurance and so would face serious problems should you require medical attention.