Your partner is quite right, they do, either dislike him or dislike having children who are half Irish, but we choose our partners for ourselves and not for our parents and, while it is nice if families can all be friends together over generations, your problem is quite common.
My grandmother did not want my father to marry my mother. Both families were Irish/English and catholic, so where could the problem be? Well, my mother was pretty vivvacious, liked the theatre nd the arts and my grandmother did not trust women like that 'no better than she ought to be'. She didn't like me either - too much like her mother.
Then thing to do is accept that while your situation is uncomfortable, how your parents feel is irrelevant. You are with the man you love and have his children, your parents do not like it, that is their problem, not yours. Ignore it, build your life with your partner and children and getting on with his parents.
It may well be that once your parents realise, that you are happy with your partner and have given up worrying about their lack of approval, they will tone their reactions down. Currently you are a puppet on a string in their hands. Every time they are nasty, you get upset. They can keep thinking that one day you will leave your partner and come back to them because you respond to all their hostility by getting upset an trying to curry their favour.
My mother left my grandmother to her hostility and I did the same. It could be difficult, but in the end it was my grandmother who was the loser, not my mother or I, my mother had a happy marriage with a husband she loved and loved her and her family and as part of their family, it would have been nice for me to have had a grandmother who was less critical, but I could live with her unpleasantness.
Your reaction must be the same, it would be nice to be on good terms with your parents, but since they are so hostile to your partner and children, leave them to it. Enjoy your family life, get Irish passsports for your children and enjoy your family life. When we marry we separate from our parents and turn to our partners to form a new household.
You have never done this. Now is the time to gently tell your parents to get lost and stick to your partner and family.