I am from a non-visa required country. I will be going to Ireland for work with General Employment Permit. Based on this background, could I ask a few questions?
1. Could my family (my wife and a child) come to Ireland visiting me for more than 90 days?
2. If they can, how long would they be extended normally?
3. Can they travel to other Europe countries for a few months, and then go back to Ireland visiting me during their stay?
4. What could be the factors to affect the decision of how long they can stay?
I have proofs (bank statements) for immigration officers that my family can be well financially supported by me. Thank you.
You'll find it useful to read through the Expat Arrivals page on visas for Ireland. Other information, as well as factors influencing the strength of your application, can be found on the Irish Naturalisation and Immigration Service website.
Faimilies visiting those with General Employment Permits for less than three months apply for the 'Short Stay 'C' Visa'.
Families staying longer than 3 months need to apply for the single-entry 'Long Stay 'D' Visa'. As this is a single-entry visa, it will not allow your family to travel outside of Ireland.
After your family is granted a Long Stay D Visa, then they need to apply for a 'Multiple Journey' Visa if they want to travel outside of Ireland. This is granted at the discretion of the Visa officer.
Travel in the EU
Also note that Ireland, although part of the EU, does not participate in the Schengen visa system. Your family therefore won't be able to freely travel to Shengen countries with a Multiple-Entry Long Stay Visa.
They will have to secure a Multiple-Entry Shengen visa to do so.
Which country is your wife from? And which country are travelling from? It might affect how applicable the information is below.