Originally Posted by
GFrye
Ireland isn’t part of the Schengen area, so the traveler would go through UK immigration at MAN and then travel to Dublin without any additional immigration checks since Ireland is part of the Common Travel Area. Since Brexit will be delayed, there will be no short-term changes.
Thank you for the correction. ^ I'd forgotten about that distinction, and it's definitely important.
As for a Brexit delay -- that certainly seems possible, given today's vote by the UK Parliament, but it wouldn't take effect without EU approval. However, what I've read is that the CTA agreement, because it's bilateral with Ireland and not part of the larger EU freedom of travel agreements, would carry through in the event of a no-deal Brexit.
That said, I still wouldn't try to make a separate-ticket transfer at MAN with two hours between flights, and I think the OP did the right thing by changing the second ticket.