It's not surprising that you feel overwhelmed. Who wouldn't want to pack up and go and live a life that looks so inviting with the man you've fallen in love. Something you would have probably done a year ago if it wasn't for your children.
What you need to focus on is firstly whether you can actually do it, and then how you can do it in a way that doesn't destroy the relationship between your children and their father.
I have been there, both as the child and the parent. As a child as I almost lost out on a relationship with my father when my mother decided to move abroad. At the time, things were bad between them (just separated) and my mum probably believed my dad was useless and I wouldn't miss being away from him. Thankfully, my dad adored me and nothing would have stopped him, so he got on a plan and went to get me back (in the 70s!). My mum realised then that she had to go back and make it work. I grew up with the difficulty of being the child of divorced parents, but I saw my dad every other week-end, and he became as important in my life as my mum. As an adult, my dad is a big part of my life still and I can't imagine it any other way.
As a parent, I found myself in exactly the same situation than you, except it wasn't a partner that was calling me abroad but a much better life with support. I had two kids and had worked it out that it would have been possible to arrange for them to come and see their dad every other week. However, looking back, I was at the time very much blinded on how I could make it work, forgetting how tedious and difficult doing so would have been. In the end, I didn't move but my life did change for the best. My kids are now teenagers and see their dad and his family every week-end and it means a lot to them.
Your first step really is to seek legal advice because my experience doing quite some research about it at the time is that the courts are not favourable to the parent wanting to move at all. They consider it from the perspective that the decision is not one to suit the parent wanting to go but that that parent really has no option and that it is still better for the children to be with that parent.
They will most likely consider whether indeed your OH is in no way able to move his business to the UK. They will assess whether your relationship is solid enough and whether he really will be prepared to support you in Ireland. They will consider how well planned your move is and then of course, this will be outweigh with the case your ex puts forward, ie. will he ask for residence of the children and what life and stability will he be able to offer.
What will go against you is the fact that your relationship is not well established at all, yet you are strongly relying on him to support you and your children. What if after a couple of weeks there, you realise you can't live together and he throws you out? It will then also depends how strong a defense your ex puts up.
If you really want to make it work, my advice would be to look at moving there on your own rather than straight with him. Try to find a job there before you make the move. Show that you can be independent as you are now rather than relying on someone else. That would most likely help your case. Then show that you have really worked out a realistic schedule to allow your kids regular visitation with their dad. You'll need to look at times and costs, ie. if you are a nurse, will you be able to ensure you have time off on the week-ends so you can fly them back regularly? Will you work out a budget to show you can afford it? If you are reliant on him, how will you ensure you will always get the money to take your children back? Would it be fair if your relationship went sour, your partner stops getting your money, and you can't afford the flights any longer that your kids are then deny their right to see their father?
These are all the things you need to start thinking about if you really want to make it work. I do think it is possible but I think it won't be as fairly tale as you are, understandably, currently seeing it.