can't help with what vaccines etc are needed, but when i went down south on holiday a few years back we took missy with us to stay for the fortnight in the cottage complex. their rule was as long as she was house trained and we cleaned up after her, it would be lovely to meet her!
as for shops, as long as you are polite about it, and always ask in advance (ask someone working in the shop if its ok you carrying them), a fair amount of shops do tend to allow little dogs as long as they are in a bag or buggy (we were actually able to take Missy into a few cafes in her buggy because the owners themselves didnt want to risk leaving her outside! any time i go out shopping i take one of my girls with me (i feel better in crowds if i have company!) and ask at the door if i can carry her in- 95% of the time it is a yes, if not, i just say 'ok, thankyou' and walk on, and thats in belfast centre, and most of the bigger towns and 'citys' in co. antrim and co. Down as well as the little villages!
of course it depends whereabouts you are going; i went right down to Co. Kerry, so no really built up areas like dublin would be! heck, Shannon airport looked like a toy airport- even compared to belfast city airport!!!
yes, we unfortunately are puppymill capital (i know of 5 within a 30-45min drive from where i live
), so don't leave them unattended; and maybe invest in a ' i am chipped and spayed' tag for each! but i'd recommend that for anywhere tbh.
it really is a beautiful country though; both N & S well worth a visit!
i don't know if i could ever leave!!
also, make sure you try the traditional good ol' taters and stew! lol