Question on entering ROI from Northern Ireland.

My family and I want to travel from England for a short break to Ireland (2 Irish, 2 non-EU citizens) to meet and stay with relatives in a couple of months time. Having read lots of horror stories about the visa office responsible for issuing visitor visas (missing passports / information, really long periods of time waiting for passports to be returned etc) I figured with the money we'd spend on getting the visas, we could use that money to travel down from Northern Ireland instead and save all the hassle.

I wanted to ask whether this was a viable plan. I know there's no actual border between the countries, so wondered if we could get a bus or train down instead and how easy / difficult that might be?

Thanks.