My theory is that the concept of "groups" in RTW is quite a bit different from that of MTW. There is a high chance that it could be a bug, but it might also be a feature. The 'grouped' units in RTW have a strong tendency to try to retain its initial formation and unit positions, and thus more often than not it seems the units try to maintain the general formation while it is on the move.

The problem usually manifests when there are multiple units in groups which have different special abilities or movement speeds, and when the group is assigned to move over long distances. For instance, a group of Phalanx wielding infantry mixed with normal infantry does not respond to "run" command very well. As much, a group of missile cavalry mixed with normal cavalry sometimes fails to respond to attack inputs, because the missile cavalry may have "skirmish" mode on.

Therefore, the best method so far, is to make quick use of the "G" key and group only upon need. If the "group" command in MTW was more or less static, in RTW it is flexible. You want to keep grouping and disbanding units during battle according to the situation. Usually the static line playing the role of the "anvil" is preferred to be grouped, while the units playing the "hammer" role may be grouped initially, but quickly dispersed according to situation.