fly to dublin, hire a car, think about portmarnock, the island and county louth... travel northwards and do county down and portrush, then get the ferry over to stranraer and do turnberry, prestwick and western gailes... then drive over to fife and do the old course and kingsbarns before heading to north berwick and muirfield and flying back to dublin from edinburgh...
...this actually provides you with no long drives whatsoever...
...so you're missing the SW of ireland and a whole heap more but you can't do it all...
...other options are of course to spend a whole week in st andrews which may be more relaxing and twice as much fun