I know there are passenger lists for those leaving Scotland for the US, but are there any passenger lists for those arriving in Scotland? I am looking for the arrival record for the Batchelor family that moved from the US to Scotland about 1822.

The father was born in Scotland, moved to the US at an unknown date, married a woman in Massachusetts, then returned with his wife and young son (George Batchelor) to Scotland. According to George's obituary, his family moved to Scotland when he was 18 mos old which would be 1821 or 1822. They relocated to England in 1833, then George married Catherine Ramsay (who was also born in Scotland) in England in 1841 and moved to the US in 1843. I want to find George's parents but have been unable to find any record of them in the US (but of course it's pretty difficult when you only have a surname).