We are an American family. My husband (and only he) has dual citizenship (American/Irish).
The UK allows Irish citizens to live in the UK, which was an agreement that was in place long before the UK joined the EU. Only the UK, or the Republic of Ireland, or the EU, can stop that.
Is your husband also a British citizen? Such as born in Northern Ireland (UK) or his parents were born in NI?
Next, I will take early retirement from my civil service job and will receive a partial pension. We will also have rental income and retirement savings to live off of. Will that be enough to show financial independence, or will we need to show additional resources?
In that case your husband needs to show that he is of independent means to be able to keep you all and he must buy CSIs (Comprehensive Sickness Insurance) for each of you, every year, including for himself. He has chosen to use EU rules to bring you all to the UK and must follow those rules at all times. UK immigration rules are different.
A "self sufficient" EEA citizen and all their family members must not take welfare or healthcare from another EEA country as they are not allowed to be "an undue burden" to that country. The same with EEA student qualified persons. EU rules are all about being a "qualifed person" to have a "right to reside" in another EEA country.
The UK requires EEA citizen self sufficents and students, to have CSIs for themselves and all their family members. If they don't then they are not a "qualified person" in the UK and therefore they have no "right to reside" in the UK with their family.
Although the UK allows Irish citizens to live in the UK as a British citizen can, to bring any non-Irish, non-EU citizens to the UK under EU laws, he needs to follow EU rules, continually. If he stops doing that at at any time, then all his family members (you, your daughter and niece) lose your "right to reside" in the UK under EU rules. Normally an EEA citizen would lose their "right to reside" too, but as he will be an Irish citizen in the UK, the UK will allow him to stay.
We are thinking that either my husband or I would find some work, freelance, teaching, etc. to supplement our income. Do we have to show that we have employment?
No, your husband just needs to be a "qualifed person" at all times. He can mix and match these differnet types, as long as he follows what the UK says that type of "qualified person" must hold/do at all times.
If your husband is any type of "qualifed person" at all,then you can work. If he ceases to be a qualifed person at any time, then you are not allowed to work in the UK as you would have all lost your "right to reside" in the UK. From June 2016, working when not allowed is now a criminal offence in the UK.
For our niece who is not our biological offspring, what documentation would we need to present to show that she is our dependent?
Yes. An EEA citizen's spouse and their own children under age 21, are family members. Any others are extended family memebers. For extended family members, the EEA citizen needs to prove that they are depenendant on them. Their UK RC is given on that condition and becomes invalid if they cease to be dependant on them, or if the EEA citizen stops being a qualified person.
These are the present qualified person rules in the UK which your husband will need to understand to make sure he follows them. Be aware that the UK can change these conditions at any time and it is up the EEA citizen to keep up with any changes.
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/488449/Qualified_Persons_v3.0_ext_clean.pdfYour problem is Brexit. From when you arrive, you will need 5 or 6 years of EU laws being lawful in the UK, to reach British citizenship. It is unlikely that there will be that long before Brexit. You would have to wait and see if the UK will offer you anything.
