In US English--I'm not sure about British English--and in _horses_, this is called "pacing." It is one of a number of leg movement patterns horses have. The patterns are called "gaits." Not all horses do it. The ones that do it are called "pacers." Pacing is natural for camels, alpacas, etc. I think horses need to be trained to do it. The common gaits are walking (one leg moves at a time); trotting (alternate diagonals, front left with hind right, then front right with hind left); canter (both front legs, then both hind legs); and gallop (I am never clear on the exact difference between a canter and a gallop). Pacing is front and hind left, then front and hind right. I don't know anything about the gaits of cats or how they are named. Baby lambs have an extremely cute thing they do. They jump on all four legs at once. I think this is the literal meaning of the word "gambol." If you want to find out more about cats, use search terms like "gait" "cat" "feline" and "locomotion." Hey, I just found a paper called "Why Cats Pace on the Treadmill."

lol, your English was perfect, but it was still difficult to imagine. For any other English readers having trouble comprehending, she is asking for words regarding moving, for example, left arm and left leg at the same time, when normally you move the left arm and right leg together. I am not aware of any specific words for this. Maybe dancers have some? I guess a doctor may have some technical term such as a "unilateral gait" (one-sided method of walking). I am failing to google it.

Wow that is so specific girl!

I think trotting horses are trained to do this.