I'd like to study in Ireland for 4 months, with a Schengen visit in-between. As a visa-free national, would I need to apply for a regular visa? [closed]

Question

I plan to travel to Ireland (for a study program) for about 4 months. In the middle of this period I'll want to fly to the Netherlands for a week. I also might want to visit the UK in this period.

I don't need a visa for a short visit to Ireland (as well as the Netherlands and UK). My total stay will exceed 90 days, but each contiguous period will not. So perhaps I need a type D long stay visa.

My questions:

1. Do I need a long stay visa? Perhaps not, because I won't stay more than 90 contiguous days in Ireland? If it was Schengen, the 90-180 rule would say that I do. But Ireland isn't Schengen.
2. Single or multiple entry? According to the INIS site, long stay visas are single entry. Does it mean I won't be able to leave Ireland during this time? I can apply for reentry visa once in Ireland, but the Netherlands trip is important to me, and I want to be sure I can make it.

Notes:

1. I have an Israeli passport, allowing me to enter Ireland, the UK and EU for a short periods with no visa.
2. My wife was accepted for a 3-month post-doctorate study program in Ireland. I'm travelling with her and our 2 kids.