I do not want to dissapoint you but history is different.
Holland Exel went bankrupt and TUI stepped in to continue this company in order not to loose to many seats in that period.
Trying to figure out a name wasn't hard, it should end with ....Fly and than preferably with a Dutch tour operator under TUI flag in front af that , Arke seemed to fit in front.
So it became ArkeFly.
(With some involvement from Holland but they made that one up in Germany , in Holland it sounds a bit strange as Fly and Vlaai are rather close to much amusement of all the crew).
And so there is no real connection between Arke and ArkeFly other than that Arke was sold to TUI some time ago and ArkeFly is a TUI activity.