It is a mix between rotation and translation.
But it is hard to synchronise both types of movement.
is correct. But it can be easily visualized geometrically. I’ll try to put an image in here that may help you see the geometry involved.
Its the radius of your rocker arcs that’s the key. You must move the center of this arc (or the whole rocking horse, in your case) the same distance as this arc radius for every 90 deg. of rotation.
Another way to look at it is, you always want to keep the centerpoint of the rocker arc directly above where it contacts the “floor”.
Probably, you don’t want it to rock as much as the illustration shows, so start by dividing it by half. In the example, if you move the rocking horse 1 inch, and rotate it 45 deg. then you’ll have the same effect. If this is too much, try 3rds (or 30 deg. & .6666 of an inch.)
Simply match the keyframes for your translation and rotation keys. You’ll also want to match the interpolation type and amount of your IPO curves.
Hope this helps more than confuses.