I am having trouble pinning down the father of Robert Clark 1812 above. A general search obviously is bringing up different suggestion which is confusing me even more. How do I pin down the actual father of my Robert Clark?
That depends on where he died.
They were in Leith by 1854, when their daughter Betsey was born, and Robert was alive in 1861. Ten years later, Ann was a widow. The question is whether he died before or after her move to England. If he died in Scotland before they left, his death certificate will confirm the name of his wife and should tell you the names of his parents, including his mother's maiden surname. 
There's only one recorded baptism of a Robert Cl*rk* in Crathie and Braemar, son of James Clark and Janet Morice, baptised 1 December 1810, which is close to Robert's age in the 1851 and 1861 censuses. But that does not mean he has to be the one, because the records are incomplete and there could be another Robert Cl*rk* whose baptism record has not survived. 
There are three deaths of Robert Cl*rk*s of suitable age in Edinburgh between 1861 and 1871, none with mother's surname Morice, and two in Glasgow with no mother's maiden surname indexed.
If, however, he died in England, his death certificate won't even tell you the name of his father. I'm not even sure that it will include the name of his wife.
It's also not beyond the bounds of belief that his wife left him, moved to London, and claimed to be a widow, though it's not very likely.
From what has been discovered would you say the Anchor Mills connection is out of the question now?
I wouldn't rule it out but even if it does exist it's going to be very difficult to prove because any connection must be before 1800. You'd need to take a much closer look at the Paisley Cl*rk*s to see if there is any connection to Aberdeenshire.