This is a hard to describe observation, and it can be difficult to identify a physical cause.

Disjointedness can come from apparent incoordination, which can be neurologic or pain-related. It may relate to the inability to change or hold leads. It can be caused by an inability to round and collect. A horse's own physical ability and experience comes into play here too, as do even more obscure training, rider and environmental factors (footing).

Professional riders and trainers are inclined to pick up on subtle changes in a horse's movement that indicate something is wrong.

WHAT YOUR VET DOES

The vet's role is to first rule out lameness with a thorough lameness exam. Along with that may be assessment of the back and saddle fit, and an assessment with the rider up so that the problem can be observed first hand.

One trick I have resorted to over my practice career, if I cannot find an obvious reason for a subtle issue under saddle, is to have the rider really study the problem, consider when it occurs and what it feels like, and then put horses on pain relieving doses of bute for a few days - a bute trial. If there is a noticeable change in the horse while on bute, then there is more reason to suspect pain as playing a role in the behavior.