Normally yes. But the relationship between these three is sometimes a bit more complex. Some are owned equally in partnership and others have majority share weightings, while others are owned either between two of the three or outright and a few with other owners.
In the past some of their horses have alternated colours (it's not always clear whether the percentage ownership has changed or not) for those owned equally, in the same way as Denman for instance alternates colours between his equal joint owners.
Consequently some horses are entitled to wear two (or in theory even more) sets of first colours. And it is an option whether to run them in another first set or the second-colours of the original set (if you see what I mean). I didn't mean to suggest that this was necessarily the case in the Dante though.
I've noted that when two equally owned horses run they tend to run in alternative first colours rather than necessarily the first and second colours (although it's difficult to know which ones are owned equally from those that are unequal).
If they want to make it clear that one is a second string, they seem to try to use second colours rather than alternate first sets.
Using Down To The Woods (admittedly not a Coolmore horse) as an example – owned in joint equal partnership. I had my own set of colours, Graham had his and we had joint-partnership colours. When owned by us he ran in joint partnership colours, but in theory he could have run in any of three first sets.
Had we ever run a similarly owned horse in the same race we’d have the option of running the two in any of the three first sets, or a first set and the second colours for that set.