In reply to Flinticus:
> Could we get caught up in delays at the border?
Yes, certainly.
> What paperwork would be needed? My wife (English) does not have a passport. Will that be a problem?
You'll need passports; there's still time to sort hers.
> Will driving under UK licence in Ireland be an issue?
Looks as if this'll be OK for Ireland:
https://www.moneysavingexpert.com/team-blog/2019/03/driving-abroad-after-br...
> Medical care? Would we need medical travel insurance?
Yes, EHIC won't be valid in ROI if there's no deal.
All of these things can be sorted and will be manageable - just more expensive and more hassle, with more chance of getting caught out by failing to sort something.
But personally, I wouldn't entertain travelling between the UK and EEA (or for that matter further afield - there could easily be knock-on disruption) so close to the brexit date, unless essential - waiting for the initial chaos to settle seems a much better plan.