Hello Sandra !
You will definitely need a visa, I suggest that you strongly look into this, it's quite complex.
As you are not married if could me more complex even. ( you will have to prove that you've been living together for 3 years I think)
You would have to apply for a resident permit as a family member of a EEA national IF you're boyfriend as an Irish passport. What is the nationality of your children ? They might need a visa too. If you're boyfriend is only British that could be very tricky. As he would be require to earn the equivalent of 23 000 £/year.
You will have to spend both a lot of time here > Â Â and find the right visa for your unique situation.
There are some unofficial dedicated forums too, where people currently applying or in your situation can help.
I don't think I 'll be able to help you fully, as my application ( my husband is from India, I am French) was a couple of years ago, and regulations change a lot.
As for NI, being from Mexico you will miss the sun and the warmth. Northern Ireland is rainy, and cold in comparison. It's a nice place to live though.
If you have specific questions, don't hesitate.
Good luck !
Elinore
