Anyone can correct me if I'm wrong, but I have seen in a few cases people are focusing on where the child was born. If both parties agree to move to another country to live and raise their children there, then where the child is born is irrelevant. The whole point of The Hague is to return children to their habitual residence, so that the governing authority can decide custody. Habitual residence to me is wherever both parties decided to raise their child. The hague is not supposed to be used to determine custody, as all of us have seen this is not what actually happens.
From what you have said, and again you still have not given us much information. The information that you have given us is not doing you any justice, because we all are confused and do not understand your case. From the sounds of it, this is not an international abduction case nor international custody case. You agreed to live in Ireland with your then husband and children, or you married him there and had your kids there. That information is still unknown, because you have not given us a direct answer to WHERE WERE YOUR KIDS BORN? Regardless of where they were born you both agreed to live there, at some point. Unless you can show proof that some how this man forced you or coerced you to move to Ireland, then you are not going to get much help from anybody.
All this sounds like is an ugly divorce and custody matter. These things go on everyday in America as I'm sure in every other country. They are ugly, depressing and mentally draining. However they do go on everyday and your case does not seem any different then a normal custody case. The fact that you are from America ( atleast I think you are), and you live in another country, makes this case more difficult but you did agree to move there (again this information is still unclear).
The fact that you guys are now separated and that he mentally abused you for years, does not give you the right to take BOTH of your guys children away from him. You say he is telling your kids certain things that you ran out on them. Number one you just admitted to running out on them. " He has told my kids I ran out on them, knowing the truth that I was very depressed and had to get myself sorted first before I could even think of fighting." As a parent myself, once you give birth you now have a lifetime commitment to your children. There are no taking breaks to sort things out, if your a mother or father your a mother or father for life 24 hours a day, 7 days a week 365 days a year. Number two if he is indeed lying to your kids and trying to fill their heads with negative thoughts about you, that is a form of mental abuse called PARENTAL ALIENATION. I do not know the laws in Ireland, but I believe in Brazil this is illegal and against the law there.
This is just my two cents you can take it or leave it, but you just admitted to being depressed. You have admitted to leaving your children, because you were depressed and needed to sort things out. Based on that I would say you do not deserve and should not be granted anything but joint custody and that is pushing it. You with out a doubt should never be granted full custody after what you just said, and with no proof of any abuse done to your children by your ex-husband. Parenting when not married is extremely hard especially when one parent is not from the country. You can not take back having children with this man, and that means that you will have to just suck it up and make due for the health and happiness of your children. Unfortunately in your case and most cases like yours, one parent is going to get the sh*tty end of the bargain. In your case because you are not from that country as far as I know, that person is going to be you.
You sound like you are on the verge of abducting your children, and taking them away from their father. I highly and whole heartedly suggest before you do anything stupid to think of your CHILDREN first, and not yourself. Your children need both parents. Unfortunately for you it is going to be much harder, but I suggest you fight to survive, fight for your kids to have both parents, and fight to make sure that both parents live in the same country.