oh i so remember this game and was trying to explain it to my kids who are now at that age.
It was called Yogi here in Canada and we played for hours.
We used a piece of 1/4" elastic about 8" long and knotted it together to form a ring. The elastic was then strung between the ankles of 2 people who then stood with their feet about a foot apart and leaving about 4" between the two persons who stood facing each other. It is true we did also play it using two chairs from the kitchen table whose legs were not much wider really than a person standing with their feet apart. I don't recall any rhymes as much as the moves. The jumper would jump into the middle with both feet and then jump to the outside. Then they would jump with one foot in the center and one foot to the right and then switch so the left foot was in the center and the right on the outside then they would jump to one side and while holding their left foot under the first elastic closest to them they would hook that elastic and bring it over the other one and then they had to jump into the middle with both feet inside the elastic while it twisted like a diamond around them. Then with both feet jump up and out but they had to land on the elastics and trap them under their feet and hold them to the ground. Then that is all I can remember right now but the game was definitely called YOGI>