I wish I had better news, but the Scots and Irish jumped across the Irish Sea in both directions over hundreds of years, with little or no record keeping, just as they did in and out of England and Wales. No border control, no passenger lists, nothing official.
The other problem is that a lot of Irish (and Northern Irish) records have been destroyed. Pretty much anything before the 1850's is pot luck.
It's not all doom and gloom, if your family owned land (or businesses), or were in the military, you have some avenues open to you. Likewise if you can follow their religion backwards the church records might offer some clues. Catholic, Presbyterian, Church of Ireland, Church of Scotland....
I'm having the same issues with Clarks through the ages, so I feel your pain.