Why can't Ireland trade with you, when UK leaves the European Union?
There is no obstacle to doing so, but the two countries (Ireland & UK) have to pay higher customs duties.
The Irish adopted the Euro as a medium of exchange and I believe it is almost impossible to leave the EU and return to their old currency.
You still have the British Pound, it is a lot easier.
However, it is strange, that 3+ years after the referendum, you still have no exit plan.
I have the feeling, your government doesn't want to leave, you are trapped in EU and you just delay it.
I don't believe there will be a deal. Deals include a whole load of political stuff, and we voted to get rid of that. I think there will be a number of trade agrements, and if the EU doesn't change its attitude, then most of them will go elsewhere. The UK dropped its food standards when it entered the EU, and hopefully we will be able to regain those. Much of the quality food at the moment is still produced to the old standards, and if this continues, then the EU farmers and producers will be the losers.
With regards to Southern Ireland, there is an enormous trade with the UK, and they will have a severe economic downturn when we leave the EU if they are not allowed to continue to trade with us. The EU hasn't done them any favours, and in my opinion, their best option would be to leave the EU, and to become a self-governing country again. There is a wealth of talent and resources on the island, and they are quite capable of earning their keep in a competitive world.