This seems a lot of driving with kids. From my perspective it seems to be trying to do it all at once, take it easier, explore the peninsulas, walk about the beach a bit and do the rest on subsequent trips.

Between Galway & Donegal you need to pass Sligo and will be within an hour of the Marble Arch caves, perhaps you might consider your sequence. Or perhaps skip the Giants Causeway (see above) and spend more time in Fermanagh.

In Belfast the W5 science centre might be of interest to kids
http://www.heritageisland.com/attractions/W5.htm