How should multiple Harvard references with same first author but different coauthors be made?
As eykanal said, journals usually provide their own formatting, and personally, I use latex/bibtex, so I tend to assume this kind of problems will be solved automatically.
That being said, in the case you describe, I would expect the ordering to be (first name, year), and in the case where there are multiple references with the same first author for the same year, then to use (Barton et al., 1980a) (Barton et al. 1980b). So your example would be:

Barton, D. H. R.; Dowlatshahi, H. A.; Motherwell, W. B.; Villemin, D. V. (1980). &quot;A New Radical Decarboxylation Reaction for the Conversion of Carboxylic Acids into Hydrocarbons&quot;. J. Chem. Soc. Chem. Commun., p. 732.
Barton, D. H. R.; Crich, D.; Potier, P. (1985). &quot;On the mechanism of the decarboxylative rearrangement of thiohydroxamic esters&quot;. Tetrahedron Lett. 26, 5943.

and the two references (Barton et al. 1980) and (Barton et al. 1985). That way, when I know I need to look first for the first name, and then to the year. Now, if let's assume that there is another reference by Barton and Alice in 1980, then you would have:

Barton, D. H. R.; Alice (1980a). &quot;Bla bla&quot;, p2.
Barton, D. H. R.; Dowlatshahi, H. A.; Motherwell, W. B.; Villemin, D. V. (1980b). &quot;A New Radical Decarboxylation Reaction for the Conversion of Carboxylic Acids into Hydrocarbons&quot;. J. Chem. Soc. Chem. Commun., p. 732.
Barton, D. H. R.; Crich, D.; Potier, P. (1985). &quot;On the mechanism of the decarboxylative rearrangement of thiohydroxamic esters&quot;. Tetrahedron Lett. 26, 5943.

and the references would be (Barton et al., 1980a) and (Barton et al., 1980b).
As for the question whether you should put the one with Alice first or second, it does not really matter, since the reference is unique anyway, but in this case, I would go for the month of publication if you have it, otherwise with the alphabetical order of the second author (and of the third one if the first two authors are the same, and so on).